kunci sukino 3a bab 1

- 1 -

A. Evaluasi Pengertian atau Ingatan

1. C. x6+c

dxx56 =66 x6+c

= x6+c

2. B.na xn+c , dengan n≠0

cxn

adxax nn 111

11

=na xn+c , dengan n≠0

3. B. cxn

an

1)1(

dxaxdxxa nn

cxn

a n

1

)1(

cxn

an

1)1(

4. A.41 z4-z3+

21 z2-3z+c

dxzzz )33( 23

=41 z4-z3+

21 z2-3z+c

5. B. cx 311

45

cxdxx 31

31 1

3435

35

cx 311

45

6. A. cxx

23

322

cxxdxxx 23

21

32

12)2( 12

cxx

23

322

7. C. 0

cxxxdxxx 5342

31)51(

A=1 B=1 → A-B=0

8. A. 0

dxxdxx

xx )12(22

23

cxx 2

A=1 B= -1 → (A+B)2=0

9. C. 0

cxxxdxxx

31

32

31

3165 35

24

A=31

B=32

D=31

→ A+B+D=0

10. A. ctt

3311

dt

ttdt

tt

424

2 111

ctt 33

11

B. Evaluasi Pemahaman dan Penguasaan Materi

1. a. cxxxx 38

38

38

35

83

83

b. xxxxx 253

22 35

35

32

cxx 253

35

c. cxxxx 10101011

101

101

d. cxxxx 5554

53

53

33

e. cxxxx

221

f. 423 3232 xxxxx

cxxxxxx 422422

41

23

41

23

g. 524 2323 xxxxx

cxxxxxx 5252

51

351

3

h. xxxxxxx 52345234 23423

cxxxxxxxx 55 234234

BAB IINTEGRAL

Latihan KompetensiSiswa 1

- 2 -

2. a.

cxdxxxx

dx2

12

3

2

cx

2

b. ctttdttt 322

31

3)23(

c.

dxxxxdxx

xx 3455

2

2525

cxxx

234

41

45

cxxx

234

131

45

d. dxxxx )1634( 23

cxxxx 234 2

e. cx

xdxx

x

1321

2 32

2

f. dxxx 1612 23

cxxx 34 23

g.

dxxxdx

xx 33

33 105

25

cxx 24 545

h.

c

xxxdx

xxx

1511

2 252

4

3. a. cxdxxdxx 49

45

944 5

b.

cxdxxdxx

313

4

313 4

c. cxxxdxxx

53532 12

23

d.

dx

xxx 2

21

cxxxx 441 2

e. dxydxy

yy 22

22

2112

cxy

x 213

f.

cxxxdx

xx 2

32

212

g. dxx

xx 5531

cxxxx 211

111022

h. cxxdxxx 3623

613

4. a. dxxxdxx 121 2422

cxxx 35

32

51

b. dxxxxdxx 323 6128)2(

cxxxx 432

41

268

c. dxxxdxx 6323 211

cxxx 74

71

21

d. dxxx 222)4(

dxxxx 642 816

cxxx 753

71

58

316

e. cxxdxxx 3623

61

)3(

f. dxxxxdxxx 7423 2)1(

cxxx 852

81

52

21

5. a. dxxxxdxxx 963323 2)1(

cxxx 1074

101

72

41

b. cxxxxdxxx 2

52

32)1(

c.

dx

xx

31

dxxxxx 2

32

12

12

3 33

cxxxx 2

12

12

32

5 26252

d. dxxxdxxx 2)1(

21

2

cxxx 23

21

3222

e. dxxx 22 1

dxxxxx 1232 234

cxxxxx 2345

21

51

f. dx

xxx )2)(1(

dxxxx 2

12

3 2

cxxx 21

23

25 4

32

52

- 3 -

A. Evaluasi Pemahaman dan PenguasaanMateri

1. a.

cxxdxx

xx 243

46

2334

b.

cx

xdxx

xx 141 4

3

6

c. dxxxxx 245327 357

cxxxxx 232

445

21

827 468

d. dxxxxx 335 232

cxxxx 3456

33

43

61

e.

dzzzzdzz

z2

12

32

7

21 22

czzz 21

25

29

254

92

f. dxxx23

cxxx 27

21

94

71

29

g. dttt2

2

cttt 23 25

524

31

h.

crrrdrr

rr2

32

52

7

32

54

721 2

i.

dx

xx

4 5

3 2 4

cxx

41

35

1653

j.

dx

xxx

12

cxx 21

25

254

2. a. dxxx

123

23

3

cxxx

25

54

23

2

b.

dx

xx 32

43

32

cxx 31

41 98

c.

dx

xx

3

3 2 64

cxx 32

35

95

12

d. dxxx 33 )1(

dxxxxx 31

34

37

310

33

cxxxx 34

37

310

313

43

79

109

133

e. dxxx 3)1(

dxxxxx 27

25

23

21 33

cxxxx 29

27

25

23

92

76

56

32

f.

dxx

xx2

34

7532

cx

xx 75

143

212 3

g.

dxx

x 2)43(

dxxxx 2

12

12

3 16249

cxxx 21

23

25

32165

18

h.

dxxx

x 3)43(

23

6414410827 23

xxxx

dxxxxx 23

21

21

23

6414410827

cxxxx

21

21

23

25

12828872554

i. dxx 4)1(

dxxxxx 1464 2234

cxxxxx 3345

34

251

j. dtt 5)119(

)119()119(91 5 tdt

ct )119(541

3. a. dxxx )3)(1(53

dxxx

59

512

53 2

cxxx 59

56

51 23


- 4 -

b.

dx

xx

32 1

dxxxx 338 33

cxxxx 249

21

343

91

c.

dt

tt

4

22 1

dttt 4221

cttt 31

31

2

d.

dxxx

xx

xx 211

dxxx

xx 2

22 1

dxxxx 234 1

cxxxx 145

41

51

4. a. dxxxx 7 5 355

cxdxx 534

529

345

b. dxxxx 10 354

cxdxx 526

521

265

c. dxxxxx 5 7 3 253

cxdxx 625

619

256

d. dxxxx 7 5 26 22

dxx 2191263

3562

dxx 79421

3562

cx 70421

356

491702

5. a. dxxxx 10 354

3

dxx15

68

3

cx 1553

5345

b. dxx

xx4

10 32 322

dxx 39

113301

1011

32

cx

83323 30

83301

1011

c.

dxxx5 3 242

dxx61

31

2

cx

673

1

726

d. dxxx 7 53 3222dxx 70

211701

3541

32 cx

79

281701

3541

7028132

B. Evaluasi Kemampuan Analisis

1. dx

xx 22 )1(11

1

= ...= ...

2. dxxx 52 1

dxx

xxxx

xxxx

1515304656

4530102346

67810

cxxxxx

xxxxx

2345

678911

25

315

430

546

656

745

830

910

11

cxxxxx

xxxxx

2345

678911

255

215

546

328

745

415

910

11

3. ...33 22 xxy dengan x≠0

...333 2244 xxxy

yxy 44 3

434

3xyyy

343 3xy

dxxydx 343 3

cx 37

7333

- 5 -

4. ...222 xxxy= ...= ...

A. Evaluasi pengertian atau Ingatan

1. D. 10

cxxxdxxx 322 23)343(

f(-3)= -9-18+27+c=10c=10

2. C. 2x3-x2+x-10

f(x)= dxxx )126( 2 = 2x3-x2+x+c

f(2)=16-4+2+c=414+c=4

c= -10f(x)= 2x3-x2+x-10

3. D. 5

cxxdxxxf 23)(

19442)4( cfc=3

32)( xxxff(1)=5

4. A. x4-x2-5

y1=f1(x)= dxx )212( 2

= 4x3-2x+c1

y=f(x)= dxcxx )24( 13

= x4-x2+c1x+c2

f(0)=c2= -5f(2)= 16-4+2c1-5=7

c1=0f(x)= x4-x2-5

5. C. x2-2xy1=f1(x)=dx2 =2x+c1

f1(x)= 2+c1=0c1= -2

f1(x)=2x-2

f(x)= dxx22

= x2-2x+c2

f(0)=02-2∙0+c2

c2=0f(x)= x2-2x

6. B. -x1 +3

f(x)= cx

dxx

112

f(1)= -1+c=2c=3

f(x)= -x1 +3

7. B. x3+2x2+x-2f1(x)= dxx 46 =3x2+4x+c1

f(x)= dxcxx )43( 12

= x3+2x2+c1x+c2

f(1)=1+2+c1+c2= 2c1+c2= -1 ... (a)

f(-2)= -8+8-2c1+c2= -4-2c1+c2= -4 ... (b)

a dan b dieliminasi, didapat:c1=1 dan c2= -2f(x)= x3+2x2+x-2

8. B.21

15

f1(x)= dxxdxxf )32()(11

=x2-3x+c1

5=0-0+c1 → c1=5f1(x)=x2-3x+5f(x)= dxxxdxxf )53()( 21

= 223 5

23

31 cxxx

5=0-0+0+c2 → c2=5

f(x)= 5523

31 23 xxx

f(3)= 5)3(5)3(23

)3(31 23

=21

15


- 6 -

9. C. 11y= dxx )14( =2x2+x+c

0=8+2+c1 → c1= -10y=2x2+x-10x=3 → y=18+3-10=11

10. D.3155 xy

cxxdxxy 32

31)1(

0=0-0+c → c=0

y=31

x3-x

m=y1(2)=22-1=3

y(2)=322

38

)2(332 xy

3153 xy


1. a. F(x)= dxx )46( = 3x2-4x+c

3=0-0+c → c=3Jadi F(x)= 3x2-4x+3

b. F(x)= dxxx )263( 2

= x3-3x2+2x+c7=0-0+0+c → c=7

Jadi F(x)= x3-3x2+2x+7

c. F(x)= cx

dxx

112

21

321

3 cc

Jadi F(x)=21

31

x

d. F(x)=

dxx2

41

cxx 3

31

41

c 3)1(31

)1(41

2

1211

1121

2 cc

Jadi F(x)1211

131

41 3 xx

e. F(x)= dxxx )2)(1(

= dxxx )23( 2

= cxxx 223

31 23

c 6227

923

c=0

Jadi F(x)= xxx 223

31 23

f. F(x)=

c

xxdx

xx 2

212 2

2

9=2+1+c → c=6

Jadi F(x)= 62

21 2

xx

g. cxxdxxxF32

)(

c 4432

0

316

c

Jadi, cxxxF 32

)(

h.

dx

xxxF 2

3 23)(

cx

x 2

43 4

41

2243

1 c

Jadi,41

22

43

)( 4 x

xxf

i.

dx

xxxxF 3

4 33)(

cx

xx 225

23

23

51

c23

23

51

1

54

1c

Jadi,54

123

23

51

)( 225

xxxxF

j. dxxxF 3)2()(

dxxxx )8126( 23

cxxxx 86241 234

c 162416415c

Jadi, 586241

)( 234 xxxxxF

- 7 -

2. a. cxxdxxxg 21

23

)13()(

b. cxxdxxxg32

)(1

c.

dx

xxdx

xx

xg 33

41 11

)(

cx 21

21 2

d. dxxxg )32()(1

cxx 32

e. cxxg 34

)(1

cxx 32

73

f. cxxdxxxxg 2321

21

31

)()(

3. a. cxxdxy 22

213 2 cc22 xy

b. cxxdxxy 2

21)1(

2131

213 cc

213

21 2 xxy

c. cxxdxxy 2

21)1(

2111

213 cc

211

21 2 xxy

d. cxxdxxy 2

23)13(

2121

233 cc

212

23 2 xxy

e. cxxdxxy 32

311

3231

313 cc

323

31 3 xxy

f. cx

dxx

y 112

110 cc

11 x

y

g. cxxdxxy32

c 4432

5

31

c

31

32

xxy

h. dxxxy 123 2

cxxx 23

11110 cc123 xxxy

i. dxxxy 164 23

cxxx 34 26216168 cc

62 34 xxx

j. cx

dxx

y21

21

2

341

43

2 cc

321

x

y

4. a. dxxxF )14()(

cxx 22131820 cc

12)( 2 xxxF9128)2( F

b. dxxxxF 126)( 2

cxxx 23250005 cc

52)( 23 xxxxF1952416)2( F

c.

c

xxdx

xxF 111)( 2

3113 cc

31)( x

xxF

2143

212)2( F

- 8 -

d. xdxdx

xdF6

)(

123 cx

000 11 cc

23)(

xdx

xdF

2323)( cxdxxxF

880 22 cc

16)2(8)( 3 FxxF

e. 122)(

cxdxdx

xdF

3023 1 cc

32)(

xdx

xdF

dxxxF )32()(

22 3 cxx

7315 22 cc

73)( 2 xxxF17764)2( F

f. cx

dxx

xF21

21

)( 2

31

161

67

cc

31

121

)( x

xF

121

131

141

)2( F

g. dxxxxF )204)(1()(

dxxx )20164( 2

cxxx 20834 23

32

3620834

10 cc

32

3620834

)( 23 xxxxF

32

364032332

)2( F

31

25

h. dxxdx

xdF)16(2

)( 2

dxx )212( 2

13 24 cxx

5005 11 cc

524)( 3 xx

dxxdF

dxxxxF 524)( 3

224 5 cxxx

35112 22 cc

35)( 24 xxxxF19310416)2( f

Soal Aplikasi Bidang Geometri

5. cxxdxxy 3)32( 2

2992 ccPersamaan kurva:

232 xxy

6. dxxxxdxxxy 23422 2

cxxx 345

31

21

51

00000 ccPersamaan kurva:

345

31

21

51 xxxy

7. dtkttF )25()(

cktt 2500050 2 cck

01151 k4k

245)( tttF

8. cxxdxxxF 23)(

509924 cc

502)( xxxF

9. a. dxxxy 583 2

cxxx 54 23

c 15362742c

254 23 xxxy

- 9 -

b. Akan dibuktikan (2,0) memenuhi persamaankuva tersebut.

2252420 23 2101680

00 (terbukti)Jadi, (2,0) melalui persamaan kurva

254 23 xxxy

10 . cxbaxdxbxay 2

2)(

0000 cc2

2xbaxy

1)0( ba1a

22 )1(2

)1(1)1(2

)1(3 bba

42

13 bb

22xxy

11 . 1236 cxxdx

dxdy

01212 11 cc

23xdxdy

2323 cxdxxy

484 22 cc

43 xy

12 . 21 3145)( tttF

cttttF 3275)(

Sumbu simetri37

614 t

c

27343

949

737

525

732675)(

27326 32 ttttFc

13. dxxxf )34()(

cxx 32 2

0)(1 xf034 x

43

x

c

43

343

281 2

c818

89

81

45

810

c

45

32)( 2 xxxf

Soal Aplikasi Bidang Mekanika

14. dttadttv )210()(

1210 ctt

12001000)0( cv

01 c210)( tttv

dtttts )10()( 2

232

31

5 ctt

0)0( s

232 0

31

050 c

02 c

32

31

5)( ttts

Benda akan berhenti ketika 0)( ts

031

5 32 tt

0151

15 2

tt

t=0 t=15Benda itu akan berhenti ketika 15t

15. dtttv )218()(

1218 ctt

20)0( v

10020 c201 c

2018)( 2 tttv2036108)6( v

sm92

- 10 -

2018)( 2 ttts

223 209

31

cttt

81)3( s

26081981 c512 c

5120931

)( 23 tttts

16 . a. dtts 3

1

)36(

3063633 31

2 tt

b. 4

2

2 23 dttts

68128042

23 tt

c. 9

4

5 dtts

3135635

32 9

4

ttt

3227

d. 5

0

)22( dtts

152 50

2 tt

e. 4

0

2 23 dttts

4

0

23 223

31

ttt

315824

364

17 . Total biaya = xdx)005,0064,1(

cxx 20025,0064,1biaya awal = 16,3

Total biaya = c 200025,00064,13,16c

Total biaya = 3,160025,0064,1 2 xxRata-rata biaya

xx 3,160025,0064,1

18. Total biaya )(xf

dxxx 26602

cxxx 32 2302Rata-rata biaya

xcxx 22302

19. Fungsi pendapatan total )(xR

dxxx 2268

cxxx 32

32

38

Fungsi Demand:

xcxx 2

3238

20. Fungsi pendapatan total

cxx

dxxx

ln23232

Fungsi Demand

xc

xxx

ln23

2

C. Evaluasi Kemampuan Analisis

1. a. cbxaxy 2

cba 0)0,1( ... (1)cba 390)0,3( ... (2)048 bacba 12)12,1( ... (3)

(1) dieliminasi dengan (3), diperoleh:6b

Subsitusi 6b ke 048 ba248 a3a

96312 ccJadi, persamaan kurva adalah:

963 2 xxy

b. Sketsa grafik kurva.

8

10

12

2

2

4

4

6

6

-2-4 x

- 11 -

2. 12 xa

dxdy

31 dxdy

x

211

3 2 aa

122

xdxdy

dx

xy 1

22

cxx

2

31 yx

c

112

3

4c

42

xx

y

3. ))(( qxpxadxdy

apqxqpaaxdxdy )(2

apqxqpaaxy )(2

capqxxqpaxa 23

2)(

3

axcapqqpaa 12)(2

380

axcapqqpaa 2

2)(

31

pqqp 222

...

4. baxxdxdy

23

330 baba5332732 baba

84 a2a1b

dxxxy 123 2

cxxx 23

5.

...

6. ctdtv 3232

5003250)0( cv50c

50432)4( v178 kaki/detik

dtts 5032

ktt 5016 2

10000500161000)0( 2 ks1000k

10005016)( 2 ttts1000200256)4( s

1456 m


1. a. duuu cos36 2

cuu sin32 3

b. d1tan2

cd tansec2

c. dd sectan

cossinsec

c sec

d. d)cos3sin2(

c sin3cos2

e.

d

2cos1cos

deccoscos

cec cos

f. dxx )1(cot2

xdxec2cos

cx cot


- 12 -

g. dx

xx2sin1

sin

xdxx sectan

cxsec

h. dxxxx sin2

cxxxx 32cos

31 3

2. a. dxxx 24cos6

cxx 3

34

sin6

b. dxxx sin6cos8

cxx cos6sin8

c. dxx

x2cos

sin

cxsec

d. dxxx

2sincos

cecx cos

e. xdxxxx 2244 cossin2cossin

dxxx222 cossin

cxdx21

f. d 2cos1

c cos2sin2

g. d 2cos1

c sin2cos2

h. dxxx 1secsec 2

xdxx tansec

cxsec

3. a. xdxxF sin23)(

cxx cos23csc 002031

1c

b. xdxxF cos23)(

cxx sin23c 0sin2035

5c5sin23)( xxxF

c. dxxxF 3sec)( 2

cxx 3tan

c4

34

tan43

2

1c13tan)( xxxF

4. a. xxxF sincos)(

cxx cossin

c2

cos2

sin5

4c

44

cos4

sin4

F

24

b. xdxxxF cossin)(

cxx sincos

c3

sin3

cos321

21

c 321

21

321

21

1c

14

sin4

cos4

F

12

c. cxdxx

xxF sec

cossin

)( 2

c3

sec7

5c

54

sec4

F

25

5. a. dxxx 22 sec2cos4

xdxx 2sec22cos

21

214

cxxx tan22sin2

b. dxxxecxx sectancoscos

cxecx seccos

c. dxxecx 0cossec 2

cecxx costan

d. dxxxxecxx tanseccoscos2sin4 2

xdxxxx seccotsin2cos4

e. dxx 5tan2

dx61tan 2

dxx 6sec2

cxx 6tan

f. dxx 7cot2

dxx 61cot2

dxxec 6cos 2

cxx 6cot

- 13 -


1.a. dx

xx

xx 22

sin1sin2

sectan

= xdxxxxxx sectan2sectan2sectan 22

dxxx 1sec1tan 22

dxx 1sec2 2

cxx tan

b. dxxx

xx 22

secsin2

sectan

xdxxxxxx 222 cossin2sectan2sectan

xxxx sectan21sec1tan 22

)(coscos2 2 xxd

cxxxx 3cos32sectan2

c. dxxxecxx 2

2

sincos2coscot

ecxxxecx coscot2coscot 22

ecxdxx coscot2

dxxecx 1cos1cot 22

cxx cot2

2. a.

dxxx

xx2

33

cossincossin

...

b.

dxxx

xx2

33

cossinsincos

...

c.

dxxxxx

42

33

coscoscossin

...

d.

dxxxxx

42

33

sinsinsincos

...


1. B. aabb 32

b

a

b

a

xxdxx 3

2

aabb 32

2. C. babababa )(32

ab

ba

ab

ba

xxdxx

3

2

= babababa )(32

3. C.31

2

1

22

121)2(

21 dxxxdxxx

2

1

32

61

21

xx

61

21

342

31

4. 104

919

1

46 xxdxx 1044108


- 14 -

5. D.21

26

2

6

sincos

xxdx

21

21

1

6. C. 5

123)32( 12

1

n

n

xxdxx

12)31(32 nn

01032 nn0)2)(5( nn

5n

7. C. -1

63)23(22

2

aa

xxdxx

6)3(46 2 aa

0432 aa0)1)(4( aa

1a

8. E. 4

2

0

)(9 dtt

2

1

1

0

)(9)(9 tdtt

1

2

1

0

)(9)(9 dttdtt

4)2(2

9. D. 23

263 13

1

2 t

t

xdxx

261tt22

33t

33 32t

10 . C. 388

7

3

3 210 dxxx

7

3

24 2541

xxx

=388

11. B. -13,5

4

1

2 12153 dxxx

5,13122

15 4

1

23 xxx

12. A. 2

xdxx cos3sin0

0sin3cos xx

2)01(01

13. A. 4

2

0

cos)tan5(

xdxx 2

0

sincos5

xdxx

20cossin5

xx4)10(05

14. A. -6

0

sin)3(cot xdxx

0

sin3cos xdxx

0cos3sin xx 6)30(30

15. A. -2, 0 dan 3

n

dxxx1

2 623

46 123

nxxx

4611623 nnn0623 nnn

0)2)(3( nnnn= -2 n=0 n=3


1. a.5

0

25

021

cxxdx

)0(225

cc

225

b.3

1

43

1

3

41

cxdxx

2041

481

cc

- 15 -

c.5

0

35

0

2

35

5 cxdxx

)0(3

625cc

3625

d.3

2

3

22

1 c

xxdx

cc

21

31

61

e.2

1

34

2

1

3

43

cxdxx

cc

43

1643 3

14,111643 3

f.3

1

23

1

223

23 cxxdxx

cc 2

23

62

27

8

g.4

12

4

13

1632 c

xdx

x

15)16(1 cc

h.

2

1

23 234 xdxxx

2134 2 cxxx)211(4816 cc

30

i.

1

1

42 42 dxxx

1

1

53

54

32

cxx

54

32

54

32

c

51

31548

152420

58

34

j.3

23

32 21111

c

xxdx

xx

cc

181

31

21

1

92

11822

1816918

2. a. 22424

1

4

1

xx

dx

b. 621

2)2(2

0

22

0

xxdxx

c. 2

0

22

0

2 44)2( dxxxdxx

38

31

242

0

32 xxx

d. 3

0

223 dxxx

931

33

0

32 xxx

e.

2

1

32

1

21 dttttdtt

2

1

42

41

21

tt

41

241

21

42

f. 4

1

)1( duuu

4

1

duuuu

4

1

2

52

32

uuuu

52

32

564

316

1518670

562

314

1511

715116

g. 2

0

252

0

32 1 dxxxdxxx

2

0

36

31

61

xx

340

38

332

h.

1

0

21 dxxx

1

0

2dxxx

61

31

21 1

0

32 xx

- 16 -

i.8

1

3 28

1

32

53

xxdxx

593

53

596

j.

2

1

)12)(5( dxxx

2

1

2 592 dxxx

2

1

23 529

32

xxx

5

29

32

10183

16

29

3. a. 5

1

5

1

)(2)(2 dxxhdxxh

842

b. 5

1

3)( dxxh

5

1

5

1

3)( dxdxxh

16)15(34

c. 1

5

)( dxxh

4)(5

1

dxxh

d. 5

1

)( dxkxxh

28)(5

1

kxdxdxxh

28152

4 22 k

2k

4. a. 3

0

)( dxxf

3

2

2

0

)()( dxxfdxxf

1055

b. 2

3

2

0

)()( dxxfdxxf

3

2

2

0

)()( dxxfdxxf

055

c. 2

0

2)(4 dxxf

2

0

2

0

2)(4 dxdxxf

22)02(254

d.

0

2

)( dxxf

5)(2

0

dxxf

5. a. 2

0

)1(cos

dxx

20sin

xx

21

b. 4

0

2tan1

dxx

1tan 40

x

c.

00

cossin xxdx 211

d. 2

0

)sin(

dxxx

2

0

2 cos21

xx

)10(08

2

18

2

e.

4

4

)(cos

dxxx

4

4

2

21sin

xx

322

21

322

21 22

2

f. 4

0

2cot1

xdx

1cot 40

x

- 17 -

g.

4

4

sincot2

xdxx

2sincos2 4

4

xx

h.

3

4

2tan1

xdx

3

4tan

x

31)1(3

i. 4

3

2cot1

xdx

4

3cot

x

1331

311

j.

2

4

costan2

xdxx

2

4

sincos2

xdxx

2

4cossin2

xx

2

21202

223

2

6. a. 4)12( 12

1

a

a

xxdxx

062 aa0)2)(3( aa

a= -3 a=2HP={-3,2}

b. 462)32(2 12

1

a

a

xxdxx

0862 2 aa0432 aa

0)1)(4( aaa=4 a= -1HP={-8,3}

c. 185)52( 12

1

a

a

xxdxx

02452 aa0)3)(8( aa

a= -8 a=3HP={-8,3}

d. 2421

)13(3

1

233

2 xxdxx

a

2421

29

27 23

aa

48954 23 aa0323 aa

1321

21

21211

2,1

a

HP=

2131

,2

131

7. a. 5

2

228 dttts

5

2

32

318

ttt

38416

31252540

63

11745

b. 3

12

82 dtt

ts

3

1

2 8

tt

38)81(

389

c. dttt 3

0

2 2

3

0

23 221

31

ttt

21106

299

8. a. 3

1

)2)(1( dxxxx

dxxxx 3

1

23 2

3

1

234

31

41

xxx

1

31

41

994

81

3220

- 18 -

b.

dxx

xxx2

2

dxxxx

212

xx41

1

c. dxxxx

3

12

32 1

3

1211dxx

x

3

1

2 121

xxx

1

211

31

291

326

d. 3

22

234

)1(22 dx

xxxxx

3

22

22

1)2)(1( dx

xxxx

3

2

23

31

xx

43899

3111

e.

2

1

23 5438 dxxxx

21234 522 xxxx525212208832

f. 33

223 2

3 2 125 dxx

x

23

23

3

2

33 2 363 xxx

236223336393

242363

223321

9.21

)2(1

n

dxx

21

221 1

2

n

xx

21

22

12

nn

142 2 nn0342 nn

0)3)(1( nnn=1 n=3(tm)

a. 1232 nb. 49)12( 2 n

c. 1)2( 2 n

d. 25)2( 2 n

10. a

dxx1

10)52(

105 12

axx

0452 aa0)1)(4( aa

a= -4 (tm) a= -1

1

0)12(b

dxx

012 bxx

02 2 bb022 bb0)1)(2( bb

b=2 b= -1(tm)

a. 9)21()( 22 ba

b. 1)21()( 22 ba

c. 34122 bad. 31422 ab

- 19 -


1. a.

23

23

2 76 dxxx

23

23

23 7331

xxx

2721218332329

15

272121832

319

5

2620

b.

dxcbxax2

cxx

bx

a 23

23

cba 2233

23

c.

a

a

dttt22 2

a

a

dttttt 4452 234

a

a

ttttt 42

35

21

51 2345

334455

35

21

51

aaaaaa

aaaa 42 22

aaa 83

1052 35

d. 12

2x

x

dtt

123

31

x

x

t

xxxx 11212831 23

31

311

438 23 xxx

2. dcxbxaxxf 23)(00)0( df

00)1( cbaf

cbxaxxf 23)( 21

3636)0(1 cfsehingga 36ba

36 ab

1

0

23 5ddxcxbxax

1

0

23 36)( xdxxaax

5183

364

1

0

234

xx

ax

a

5181234

aa

112

a

12a483612 b

3. 1

0

2 dxmlxbaxx

1

0

23 )()( bmdxxblamxalmlx

0234

1

0

234 bmxxblamxalmxl

= ...

4. 1

0

221

0

)66(6612 xabaxadxax

0)6( bdxxab

3310

2 )22(266 xabaxaxax

02

31

0

2

bxxab

02

322212 bababaa

0621

16 ba

ab1233

1

0

2221

0

2 2 dxbabxxadxa

13

1

0

2232

2

xbabxxaxa

13

22

2 babaa

11441089

1233

32

22

aaaaa

- 20 -

1144

108939648144 2222

aaaa

144885 2 a

8851442 a

885

12a

ab1233

885

396

885

12 ba

885

396

885

12

ba

a. 22 334 baba

12,51688512492

b. ba 38

885

3963

885

96

885

1096

885

1096atau

5. a. x

dtttxf1

2 43)(

x

ttt1

23 423

31

4

23

314

23

31 23 xxx

6524

23

31 23 xxx

43)( 21 xxxf

b.

15

1

2 43x

dttt

223 1)15(231)15(

31 xx

1154 x

xxxxxx 2015275525

3125 223

xxx 102

153

125 23

1015125)( 21 xxxf

c.

x

x

dttt 12 2

x

x

ttt 23

21

32

xxxxxx 2233

21

32

xx 234 3

24)( 21 xxf

d.

3

1

22 dtxxtt

3

1

223

231

txt

xt

)13()19(2

)127(31 2 x

x

328

44 2 xx

48)(1 xxf

e. x

dxxxt3

2

x

xtx

3

23

21

3

29

921

33

4

xxx

923

34

)( 231 xxxf

f. x

dttxt3

2

x

ttx

3

23

3

993

24

xxx

9234)( 231 xxxf

6. a. 2

0

12 )()( dttfxxf

)0()2()( 2 ffxxf

b. x

a

xxdttf 23)( 21

23)()( 2 xxafxf

)(23)( 2 afxxxf

c. x

axxdttf1

21 2)(

axxfxf 2)1()( 2

)1(2)( 2 faxxxf

- 21 -

d. x

xxxfdttf1

21 7)()(

7)()1()( 2 xxxffxf)1(f

...

e.

1

1

1 2)( dxxf

2)1()1( ff

x

fxfdttf0

1 )0()()(

3

9x

k

7. a

dttfxxaf0

)(4)(

a

xxafdttf0

4)()(

a

xxafdtxf0

4)()(

8. x a

dttfaxxdttf0 0

2 )()(

...


1. C. 1,0;)1(

1 1

nacbaxna

n

dxbax n

)()(1 baxdbaxa

n cbax

nan

1)(

)1(1

Penyebut tidak boleh nol, sehingga a≠0 dan n≠ -1

2. A. 1;0;)()1(2

1 12

nacbaxna

n

baxdbaxa

dxbaxxnn 222

21

)(

cbaxna

n

12

)1(21

a≠0 dan n≠ -1

3. E. 2

cxaxdx 3

3

cxxdx 32

3Jadi, a=2

4. C. 56 x

)65(6561

65 xdxdxx

cxx 65)65(32

61

cxxcxxf 65)65(91

65)(91

56)65()( xxxf

5. A. x59

)59()59(51)59( 66 xdxdxx

cx 7)59(351

xxf 59)(

6. B. cx 5)37(151

)37()37(31)37( 44 xdxdxx

cx 5)37(151


- 22 -

7. C. 0;)cos(1

2 acbaxa

dxbaxa

)sin(1

0;)cos(12 acbax

a

8. D. 0);sin( abax

dxbaxa )cos(

0);sin( abax

9. E. cx

31

4sin41

dxx

31

4cos

= cx

31

4sin41

10 . D. cx

415tan

51

dxx

415sec2

cx

415tan

51

11 . B.97

1

0

231 dxxx

1

0

22 313161

xdx

1

0

22 313191

xx

97

91

98

12 . D. 12232

dtan1sec45

0

2

= )(tantan145

0

d

=

45

0

tan1)tan1(32

=322

24

= 12232

13. D. c2sec21

dd 23 sectan

cossin

)(secsec d

c 2sec21

14. A. ctt 3331 22

dtttdttt 33 224

)3(321 22 tdt

ctt 3331 22

15. D.31

1

0

21

0

42 1 dxxxdxxx

1

0

22 )1(121

xdx

1

0

22 1)1(31

xx

31

16. C.8

17

1

1

3

141 dxx

1

1

3

1411

414 xdx

1

1

4

141

x

25681

256635

817

1634

256544

17. E. cxx 552 33

dxxx 59 32

553 33 xdx

cxx 552 33

- 23 -

18 . C. cx 14 3

dx

x

x

1

63

2

1

123

3

x

xd

cx 14 3

19 . B. 2881

4

0

4 sincos5

xdxx

4

0

4 )(coscos5

xxd

40

5cos

x

1281

2881

20 . A. cxxxx 41782142 22

dxxxx 417216 2

4174173 22 xxdxx

cxxxx 4174172 22


1. a. dxx 23

)2(

cx 25

)2(52

b.

)1()1(

1)1( 33 xd

xxdx

cx

2)1(21

c.

3

33 x

xdxdx

cx 32

d. )13(133113 xdxdxx

cxx 13)13(92

e. xdxx 31

2 32

323241 23

12 xdx

cxx 3 22 3232163

f. dyyy 341

44 1141

ydy

cyy 44 1161

g. dxxx 24

22 4421

xdx

cxx 22 4431

h. dxx4

)4(4 xdx

cxx 4432

i. du

u

u52sin1

2sin

)sin1(sin1

1 252

udu

cu

42sin14

1

cu 8sec41

j. 32 4x

xdx

32

2

4

421

x

xd

cx

22 44

1

2. a.

3

222 1

2 dxx

x

3

222

2

1

1

x

xd

3

22 11

x

31

81

245

2483

- 24 -

b. 1

0

21 dxxx

1

0

22 )1(121

xdx

1

0

22 1131

xx

31

31

0

c. 2

0

2cos

xdxx

2

0

)2(2cos21

xxd

2

0

2sin21

x

0

d.

3

0

3

02

2

2 9

)9(21

9 x

xd

x

xdx

3

0

29 x

329

e. 4

0

4

0

)42()42(21

)42( tdtdtt

4

0

2)42(41

t

31436

f. 4

0

21

4

0

21

)42()42(21)42( tdtdtt

4042 t

232

g.

0

2cos dttt

0

22 )(cos21

tdt

0sin21

0

2

t

h. 2

0

2

0

22sin21

2sin

dd

2

0

2cos21

121

21

i. 2

0

3 2 32)1( dxxxx

2

0

23 2 323221

xxdxx

2

0

3 22 323283

xxxx

0389

389 33

j. 2

0

5cos5sin xdxx

2

0

10sin21

xdx

2

0

10cos201

x

0201

201

3. a. dxxx 3cos2

cxx 3sin31

31 3

b.

tdtt

32

35

55

32 2

332

3tdt

ctt 4

561

c.

dxx 54

211

xdx 21121121

54

cx 51

21125

d.

32

2

32 53

53

53

)96(

xx

xxd

xx

dxx

cxx

22 532

3

e. dxxx 21

32 9

9931 32

13 xdx

f. dxxx 23sin

22 33sin21 xdx

cx 23cos21

- 25 -

g. tdttcossin 3

ttd sinsin 3

ct 4sin41

h. dxxx 2132 4

4431 32

13 xdx

cxx 4492 33

i. dxxx 2143 9

994 4214 xdx

cxx 9938 44

j. dxxx 12

)12()12(21

xdx

2)12(41

x

4. a. dxxx 65 sin12

66sin2 xdx

cx 6cos2

b. xdxx cossin8

xxd sinsin 8

cx 9sin91

c. xdxx 38 cossin

)(sinsin 8 xxd

cx 9sin91

d. dxx

x2

1sin4

xd

x11sin4

cx 1cos4

e. xdxx 3sin

xxd 33sin31

cx 3cos91

f. xdxxsincos10

xxd coscos10

cx 11cos111

g. xdxx 212 sectan

)(tantan12 xxd

cx 3tan131

h. dxxx 2sin42cos

)2sin4(2sin421

xdx

cxx 2sin42sin431

i. dsincos1 10

)cos1()cos1( 10 d

c 11cos1111

j. dx

xx

2)cos2(sin

2)cos2()cos2(

xxd

cx

)cos2(

1

5. a. dxxx 134

31

11

43 3

43

4xdx

cxx

11

21 3

43

4

b.

dxxx

105

1

105

52x

xd

cx

9

59

2

c. dxxxx 22 sincos

22 coscos21 xdx

cxx 22 coscos31

d. dxxxx 225 cossin

225 sinsin21 xdx

cx 26sin121

- 26 -

e.

dx

xx 2

10 111

xd

x1

11

110

cx 11)1(111

f. dxxx )12(sec)12(tan 26

)12tan()12(tan6 xdx

cx )12(tan71 7

g. dxxecxx 23cos23cot 2227

)23cot(23cot61 227 xdx

cx 23cot481 28

h. dxxax 322

3232

31

xadxa

cxaxa 3232

92

6. a. dx

xx

1

2

...

b. dx

x

x

1...

c. dt

tt

236

...

d. dttt 453

...

e. dxxx 12

...

f.

dxxx

xx432

2

2

3

432

32

2

221

xx

xxd

cxx

332 26

1

g. dxxx

10011

xdx 112100

cx 101

11012

h.

dttt

3

2

tan1sec

3)tan1(

)tan1(ttd

ct

2)tan1(21

i. xdxxx sincoscos3 2

)(coscos)(coscos3 2 xxdxxd

cxx 32 cos31cos

23

j. xxddx

xx

55 sin)(sin

sincos

cx

4sin31

7. a. 2

0

)( dxxf

2

1

41

0

3 dxxdxx

2

1

51

0

4

51

41

xx

209

651

532

41

- 27 -

b.

0

)( df

2

2

0

cos dd

2

220 2

1sin

821

22

83

12

8. a. xdxx sincos100

xxd coscos100

cx 101cos101

1

b. dec270 coscot

cotcot70 d

c 71cot711

c. dtansec10

secsec9 d

c 10sec101

d. d220 sectan

tantan20 d

c 21tan211

e. d3cos3sin4

3sin3sin31 4 d

c 3sin151 5

f. dxxx 3cot3cot 810

dxxx 3cot13cot 28

xdx 3cot3cot31 8

cx 3cot271 9

g. dttt 4tan4tan 68

dttt 4tan14tan 26

)4(tan4tan41 6 tdt

ct 4tan281 7

h. xdxecx 2coscot1

xdx cot1cot1

cxx cot1cot132

i. dxxx tan2tan122

...

j. dcossinsin2 2

dd cossincossin2 2

)(sinsin)(sinsin2 2 dd

c 32 sin31

sin


1.

dxxx 322 11

...

2. a.

a

a

dxxf )(

aa

a

dxxfdxxf0

)()(

Karena f fungsi ganjil)()( xfxf , maka

aa

dxxfdxxf00

)()(

0 (terbukti)

- 28 -

b.

a

a

dxxf )(

aa

a

dxxfdxxf0

)()(

Karena f fungsi genap, maka

aa

dxxfdxxf00

)()(

a

dxxf0

)(2

atau

00

)()(aa

dxxfdxxf

0

)(2a

dxxf

3. a. a

dxxf0

)(

...

b.

2

0cossin

sin

dxxx

x

...

4. a. 2

0

)(sin

dxxf

...

b.

0

)(sin dxxxf

...

5. a. 2

0

cos)(3sin)(

xdxxfxxf

...

b. 2

0

cos)(sin)(

tdttfxxf

...

6. a.

x

dtt

txx

0cos1

cos10

lim

...

b.

x

dtx

tx

0

2)sin1(0

lim

x

tdttxx

0

2sinsin2110

lim

x

tdttxx

0

2cos21

21

sin211

0lim

x

tttxx 0

2sin41

cos2231

0lim

22sin

41cos2

231

0lim xxx

xx

xxx

xx

x2

42sin1cos2

23

0lim

c.

x

dtx

tx

0

2coslim

x

dtx

tx

0

21

21 2coslim

x

xtt

x0

41

21 2sinlim

- 29 -

xxx

x2sinlim 4

121

xxx

2sin41

21lim

21


1. a. xdxx 32 sincos

xdxxx sin)cos1(cos 22

xdxxxdxx sincossincos 42

)(coscos)(coscos 42 xxdxxd

cxx 53 cos51cos

31

b. xdxx 34 cossin

xdxxx cos)sin1(sin 24

xdxxxdxx cossincossin 64

)(sinsin)(sinsin 64 xxdxxd

cxx 75 sin71sin

51

c. xdxx 2cos2sin 52

...

d. xdxx 33 cossin

xdxxx cos)sin1(sin 23

)(sinsin)(sinsin 53 xxdxxd

cxx 64 sin61

sin41

e. tdtt 2sincos

)(sinsin 2 ttd

ct 3sin31

f. xdx2sin

dxx

2cos

21

21

cxx 2sin41

21

g. dxx )2(cos4

dxx

2

)42cos(21

21

dxxx )42(cos41

)42cos(21

41 2

dxxx )84cos(81

81)42cos(

21

41

cxxx )84sin(321)42sin(

41

83

h. xdx5sin 3

xdxx 5sin5cos1 2

)5(cos5cos515sin 2 xxdxdx

cxx 5cos1515cos

51 3

i. xdx2cot3

xdxxec 2cot2cos1 2

)2(cot2cot21

2cot xxdxdx

cxx 2cot41

2sinln21 2

j. xdx2cot

dxxec 2cos1

cxx cot

2. a. 3

6

42 sincos

d

3

6

2

2cos21

212cos

21

21

d

3

6

4cos21

21

41

2cos21

21

2cos21

21

d

3

6

4cos812cos

21

832cos

21

21

d


- 30 -

b. 3

0

3 3cos

d

3

0

2 3cos3sin1

d

3

0

23

0

)3(sin3sin31

3cos

dd

3

0

33

0

3sin91

3sin31

0

c.

0

5sin tdt

0

2

sin2cos21

21

tdtt

0

2

sin4cos21

21

41

2cos21

41

tdttt

0

sin4cos81sin2cos

21sin

83 tdtttdtttdt

ttt coscos31

cos83 3

d. 3

6

2tan

d

3

6

2 1sec

d

3

6tan

63

31

33

63

32

e. 2

4

6cos

dec

...

f.

0

2 3sin xdx

0

6cos21

21

dxx

0

6sin121

21

xx

)00(02

2

g.

22 2sin

xdx

24sin

81

21

xx

0

20

4

43

h. 2

4

cossin

xdxx

2

4

2sin21

x

41

21

41

i. 4

0

22 sectan

xdxx

4

0

3tan31

x

31

j.

dxxx

4sincot1

dxxx

xdxec 54

sincos

cos

...

- 31 -

3. a. xdx3tan5

dxxx )1(sectan 23

dxxxd 33 tan)(tantan

dxxxxxd )1(sectan)(tantan 23 xdxxdxxxd tan)(tantan)(tantan 3

cxxx coslntan21tan

41 24

b. xdx4sec

dxxx )tan1(sec 22

)(tantansec 22 xxdxdx

cxx 3tan31

tan

c. xdxx sectan3

xdxxx sectan)1(sec 2

xdxxxxd sectan)(secsec2

cxx secsec31 3

d. tdt3cot

tdttec cot)1(cos 2

tdtttd

cot)(cotcot1

ctt

sinln1

cot1 2

2

e. xdxx 2sec2tan 33

...

f. xdxecx 2cos2cot 33

...

g. xdx7tan

dxxx )1(sectan 25

dxxxd 55 tan)(tantan

dxxxxxd )1(sectan)(tantan 235

dxxxdxxd 335 tan)(tantan)(tantan

)(tantan)(tantan 35 xxdxxd

dxxx )1(sectan 2

)(tantan)(tantan 35 xxdxxd

dxxxxd tan)(tantan

cxxxx coslntan21

tan41

tan61 246

h. xdx

3cot

xdx3tan

cxx coslntan21 2

i. xdx5cos

dxxx )sin1(cos 23

xdxxdx 233 sincoscos

xdxxxdxxx sin)sin1(cos)sin1(cos 22

)(sinsin)(sinsincos 2 xxdxxdxdx

)(sinsin3 xxd

cxxxx 423 sin41sin

21sin

31sin

j.

dxxx

4sincot1

- 32 -


1. a. 24 x

dx

sin2xddx cos2

2arcsin

x

x

d2sin44

cos2

2sin12

cos2 d

cd

cx

2arcsin

b. 236 y

dy

6arcsin

cos6sin6

yddy

y

22 sin16

cos6

sin3636

cos6 dd

cd

cy 6

arcsin

c. 494 2tdt

72arctan

sec27

tan27

2

t

ddt

t

49tan4sec

2449

227

d

2

227

tan149sec d

ct

c 72

arctan141

141

d.

c

x

x

dx

2arcsin

2 2

e.

cx

xdx

5arctan

51

25 2

f.

cy

ydy

43

arctan121

169 2

g. 281 x

dx

ddx

x

cos22

1

sin22

1

cos

cos22

1 d

cx 22arcsin22

1

h.

dxx

x249

2

dxx

xdxx 22 4949

2

ddx

x

sin23

cos23

2

2

2 49

)49(81

cos13

sin3

x

xdd

cxx 24941

32arccos

i. dx

x

x24

2

ddxx

cos2sin2

2sin44

cossin d

cd cos4sin4

cx

2

44

2

cx 242

j.

dxx

x2916

3

cx 4

916122

cx 29163


- 33 -

2. a.

2x

4-x² 22 4 xx

dx

ddxx

cos2sin2

22 sin44sin4

cos2 d

dec 2cos41

c cot41

cx

x 24

41

cx

x 44 2

b.

2

x x²+4

42xx

dx

ddx

x2sec2

tan2

4tan4tan2

sec22

2

d

dcot21

c sinln21

cx

x

4

ln21

2

c.

dxx

x2

24

ddxx

cos2sin2

2

2

sin4cos2sin44 d

d2cot4

...

d.

6

x x²+6

62

2

x

dxx

ddx

x2sec6

tan6

6tan6

sec6tan62

22

d

d2tan6

d)1(sec6 2

dd 6sec6 2

c 6tan6

cxx 6

arctan66

6

cxx 66arctan66

e. 225 xx

dx

ddxx

cos5sin5

2sin2525sin5

cos5 d

sin51 d

...

f.

- 34 -

W²-7 W

7 722 ww

dw

ddw

dw

sectan7

sec7

7sec7sec7

sectan722

d

tan7sec7sectan7

2

d

cd sin71cos

71

cw

w 771 2

g. dxxx 22 16

ddxx

cos4sin4

dcos4sin1616sin16 22

d22 cossin256

d2cos12cos14

256

d2cos164 2

d4cos

21

21164

d4cos21

21

64

c 4sin832

cxx

4arcsin4sin8

4arcsin32

h.

6

x 4+x²

2

324 x

dx

ddx

x2sec2

tan2

22

2

tan44tan44

sec2 d

sec2sec4sec2 2 d

cd sin41cos

41

cx

x

244

1

i.

3

2x4x²-9

2

32 94x

dx

ddx

x

sectan23

sec23

9sec99sec9

sectan22

23

d

tan3tan9sectan

223 d

dseccot181 2

2sin18

)(sind

csin18

1

cx

x

9418

22

cx

x

949 2

j. 24 16 xx

dx

ddx

x2sec4

tan4

24

2

tan1616tan64

sec4 d

sec4tan64

sec44

2 d

dseccot641 4

- 35 -

xx

4

3

sincos

641

3.

4x

16-x²a.

2

02

3

16 x

dxx

sin4xddx cos4

6

02

3

sin1616

cos4sin64

d

6

0

3sin64

d

6

0

2 sincos164

d

dd sincos64sin64 26

0

6

0

3cos364

cos64

6

0

222

641616

364

41664

xxx

3646438332

3128324

b.

4

x 16+x²

4

0 23

216 x

dx

ddx

x2sec4

tan4

4

022

2

tan1616tan1616

sec4

d

4

02sec16

sec

d

4

0

cos161

d

4

0

sin161

4

021616

1

x

x

5401

581

c.

3

x x²+9

33

322 9xx

dx

ddx

x2sec3

tan3

3

6

22

2

9tan9tan9

sec3

d

3

6

2tan9sec

d

d3

6

2sin9cos

3

6sin91

33

3

2

99

x

x

3932

3276

3816

92

3272

92

d.

- 36 -

2x

4-x²

1

02

2

4 x

dxx

ddxx

cos2sin2

6

02

2

sin44

cos2sin4

d

6

0

2cos21

214

d

6

0

2cos22

d

602sin2

1

0

2

442

2arcsin2

xxx

1

0

2

24

2arcsin2

xxx

)00(13

13

e.

6

42 4xx

dx

ddxx

sectan2sec2

31

arccos

32 4sec4sec2

sectan2

d

31

arccos

321

d

31arccos

321

6

42sec

21

xarc

63sec

21 arc

f.

2

ww²-4

8

4 232 4w

dw

ddww

sectan2sec2

4sec

4

22 4sec44sec4

sectan2arc d

4sec

4

2tan2secarc d

darc

4sec

4

2sin2cos

4sec

3sin21 arc

8

42 42

w

w

2

g. 5

0

22 25 dxxx

5

05

arcsin4sin32625

5arcsin

8625

xx

16625

)00(016

625

h.

3

124 3xx

dx

...

i.

6 x

6-x²

- 37 -

2

12

326 x

dx

ddx

x

cos6

sin6

6

2arcsin

61

arcsin22 sin66sin66

cos6

d

6

2arcsin

61

arcsin

2cos6 d

6

2arcsin

61

arcsin

2sec6 d

62

arcsin

61

arcsintan6

2

126

66

x

56663

305663

j.

3

0216 x

dx

ddx

x2sec

tan4

43arctan

02

2

tan1616sec4

d

4

3arctan

041

d

41

3

04arctan

41

x

43

arctan41

4. a.

02 2sin1

2cos dxx

x

...

b.

4

02 2cos1

2sin

dxx

x

...

5. a. 24 xx

dx

....

6. dt

tt

2

2

41

ddt

t2sec

tan

2

22

tan4sectan1 d

dec4

cossec 2

...

- 38 -

1. a. xdxsin53

...

b. 1tan xdx

112 zzdz

...

A. Eavaluasi Pemahaman dan PenguasaanMateri

1. a. x

xdx

3

dxxdz

xz3

4

4

zz

dzz

32

2

dz

zz

)3(2

23

...


1. a. dyyy 33

Cara Tabulasiy 33 y1 43

41

y

0 53201

y

cyyy 54 32013

41

b. dx

x

x

1x 2

11 x

1 2112 x

0 cx 23

134

cxxxx 1134

12

c. dxxx 233

dxxxx 6369

x 6369 xx 1 74

71

23

9 xxx

0 852

561

103

29

xxx

cxxxxxx 852852

561

103

29

71

23

9

d. dxxx 12

2x 211 x

x2 231

32 x

2 251

154 x

0 27

11058 x

cx

xxxx

27

25

232

110516

1158

132




- 39 -

e. dyyy 28

y 28y1 38

31 y

0 48121 y

cyyy 43 8121

831

f. dxxx 242

2x 21

24 xx2 2

324

31

x

2 25

24151

x

0 27

24105

1x

25

232 24

15224

31 xxxx

cx 27

24105

2

g. dx

x

x3

5

21

...

h. dxxax 222

...

i. dxxx 62

2x 21

6xx2 2

36

32

x

2 25

6154

x

0 27

6105

8x

25

23

2

61586

32 xxxx

cx 27

610516

j. dttt 24 1

...

2. a. cxxxxx cossincos

x xcos1 xsin0 xcos

b. xxxxxx cos2sincos 22

cx sin22x xcosx2 xsin

2 xcos0 xsin

c. cbxba

bxbax

bxax cossincos 2

ax bxcosa

bxb

sin1

0bx

bcos1

2

d.

dxxxxdxx 2cos

21

21cos2

xx2cos

21

21

1xx 2sin

41

21

0xx 2cos

81

41 2

xxxxx 2cos81

412sin

41

21 22

e. xdxxxdxxx 2sin21

cossin

xx2sin

21

1 x2cos41

0x2sin

81

- 40 -

cxx 2sin812cos

41

f. xdxxx 3cos3sin8

xdxx 6sin4

x4 x6sin4

x6cos61

0x6sin

61

cxxx 6sin326cos

32

g. dxxx )12cos(

x )12cos( x1

)12sin(21 x

0)12cos(

41 x

cxxx )12cos(41

)12sin(21

h. xdxx 3sin2

2x x3sinx2

x3cos31

2x3sin

91

0x3cos

271

xxxxx 3cos2723sin

923cos

31 2

3. a. 2

0

23 1 dttt

...

b.

0

2 cos xdxx

2x xcos

x2 xsin2 xcos0 xsin

02 sin2cos2sin xxxxx 202

c.

xdxx 2cos2

2x x2cosx2

x2sin21

2x2cos

41

0x2sin

81

xx

xxx 2sin

41

2cos2

2sin21 2

22

d. 3

0

cos3sin

xdxx

...

e. 2

0

2

2cos

dxx

...

f. 4

3

4

coscot

ecxdxxx

x ecxx coscot1 xcot0 xsinln

43

4sinlncot

xxx

2

21ln

42

21ln

43

- 41 -

g. 2

0

sin

xdxx

x xsin1 xcos0 xsin

20sincos

xxx 1

h. 8

12

3 2cot

ydy

...

i. 4

0

2 sin

xdxx

2x xsinx2 xcos

2 xsin0 xcos

40

2 cos2sin2cos

xxxxx

)200(24

232

22

2232

)8(2

j.

0

3 332 sincos dxxxx

0

2 sincos xdxxx

0

2 2sin21

xdxx

2x x2sin21

x2x2cos

41

2 x2sin81

0x2cos

161

0

2

2cos81

2sin4

2cos4

xx

xx

x

481

81

4

22

4. a. xdxln

...

b. xdxx ln2

...

c. dxex x23

3xu dxxdu 23

2xedv 2

21 xex

v

...

5. a. dxxe x3

x xe3

1 xe3

31

0 xe3

91

ceex xx 33

91

3

b. dxex x3

3x xe

23x xex6 xe

- 42 -

6 xe0 xe

xxxx exeexex 663 23

cxxxe x 663 23

c. dxex x3

3x xe23x xe

x6 xe6 xe0 xe

xxxx exeexex 663 23 cxxxex 663 23

d. xdxx sin4

xxxxxx cos12sin4cos 234 cxx cos24sin24

e. xdxx cos4

xxxxxx sin12cos4sin 234 cxx sin24cos24

f. dxxt )52sin(3

3t )52sin( x23t )52cos(

21

x

t6)52sin(

41 x

6)52cos(

81

x

0)52sin(

161 x

)52sin(4

3)52cos(

21 2

3 xt

xt

cxxt )52sin(83

)52cos(31

6. a. 2

0

2 dxxe x

2

0

22

21

21

xx exe

210

21 44 ee

21

21 4 e

b. 4

0

3 4sin

xdxe x

...

c. 4

1

sec dxxarc

...

d. 1

0

arcsin xdxx

...


1. a. 3

0

2 2dxxL

3

0

3 231

xx

1569

b. 4

0

24 dyyyL


- 43 -

4

0

32

312

yy

332

36432

c. dxxL 9

09

032

xx

18

d.

1

0

230

3

23 3232 xdxxxxxxL

0

3

234 332

41

xxx

1

0

234 323

41

xxx

323

41

27184

81

2124

2. a. 4

1

2xdxL

1541

2 x

b. 5

1

)12( dxxL

512 xx 20020

c. 7

4

62xL

742 6xx 1587

d. 1

0

1 xdxL

1

0

2

21

xx

21

3. a.

-2 1 2

4

x

y

2

1

24 dxxL

2

1

3

314

xx

311

388

314

377

b.

-2 1 2

4

x

y

dxxL

1

2

24

1

2

3

31

4 xx

388

314

343

37

12

c.

- 44 -

x

y

-3

9

0

3

2)3( dxxL

0

3

3)3(31

x

9

d.

x

y

-3 2-4

1114

3

2

3

212 xxL

2

3

32

31

2112

xxx

)278(31)94(

21)5(12

335

25

60

3211

21260

6550

e.

1

4

x

y

3 4

3

1

24 dxxxL

3

1

32

312

xx

326

16

322

4. a.

1 x

y

-1

1

1

1

21 dyyL

1

1

3

31

yy

34

32

32

b.

- 45 -

x

y

1

-9

3

3

1

0

2 93 dyyL

103 9yy 8

c.

4

x

y

2-2

2

2

24 dxxL

2

2

3

314

xx

388

388

332

31616

d.

x

y

2-3

514

2

3

26 dxxxL

2

3

32

31

216

xxx

9

2918

38212

214

32219

6520

e.

1 x

y1

1

0

2 122 dxxxL

1

0

23 131

2

xx

32

4

f.

1 x

y

-1

10

-10

1

0

3 92 xdxxL

219

29

412

1

0

24

xx

- 46 -

5. a.

2

0

242 dxxL

336

3142

2

0

3

xx

b.

8

131

dyyL

8134

43 y

4111

4312

c.

dyyL 5

11

3

161132

5

1

yy

d.

dxxxL .40

2

2 0

2

23 231

xx

32108

38

e.

dyyL 2

0

2

38

31 2

0

3 y

f.

dyyL 5

112

2

321134 5

1

yy

- 47 -


1. a.

dxxxL 392

3

2 dxxx

2

3

262

3

32

31

216

xxx

3531

521

5.6

335

2530

6520

3211

21230

b.

dxxxL 2

1

22

2

1

22 xx dx2

1

23

21

31

2 xxx

3.21

9.31

3.2

21

423

36

c.

dxxxL 1

0

2

61

31

21 1

0

32 xx

d.

dxxxL 1

0

32

21

41

212 42

xx

e.

dxxxL 4444

0

2

4

0

2 4xx dx

4

0

23 231

xx

332

36432


39 2 xx062 xx

023 xx3x ; 2x

xx 22022 xx

012 xx2x ; 1x

xx 44 2

042 xx 04 xx

0x ; 4x

- 48 -

f.

2

0 222 dx

xL

0

2

3

6122

xx

316

3442

g.

dxxxxL 2

0

2

dxxx 2

0

2 .2

2

0

23

31

xx

34

384

h.

1

2

22 xxL dx1

2

23

21

312

xxx

214

2336

i.

2

1

22 dxxxL2

1

32

312

21

xxx

21436

23

j.

56 2 xx0562 xx

051 xx1x ; 5x

Jika digeser menjadi

5

1

2 56 dxxxL5

1

23 5331

xxx

20723

12 y

321052

3141

xxx 2

022 xx 02 xx

0x ; 2x

xx 22022 xx

012 xx2x ; 1x

xx 22022 xx

012 xx2x ; 1x

- 49 -

2. a.

10

112 dxxL

361134 10

1

xx

b.

0

4

2 4yyL dy0

4

23 231

yy

332

323

64

c.

4

2

2

42

21 dxyyL

4

2

32

1212

41

yyy

176203

d.

42

2

yy

822 yy

0822 yy 024 yy

4y ; 2y

4

2

2

24 dx

yyL

4

2

32

61

421

yyy

121224

3. a.

dxxxxxL 26 24

0

2

4

0

2 82 xx dx

4

0

23 432

xx

36464

3128

- 50 -

b.

1

0

32 dxxxL

121

41

31 1

0

43 xx

c.

dxxxxL 25

0

210 dxxx

5

0

2210

5

0

32

325

xx

3125

3250125

4. a. 22 xx022 xx

012 xx2x ; 1x

b. 22 yy

022 yy 012 yy

2y ; 1y

c.

4

cossin xxL dx

4

sincos xx

21221

221

01

d. 1

0

3

41

2 xxL dx

1

0

24

81

41

2

xx

41

81

.2

e. 3

2

2 62 dxxxxL

3

282 dxxx

3

2

23 831

xxx

31

334053

35

f.

0sinsin22 xxL dx

0sin2 x dx

4cos2 0 x

g. 2

0coscos24

xxL dx

4sin4 20

x

h. 56,206

56,26cossin22 xxL dx

360

56,206sin2cos xx dx

56,20656,26sincos2 xx

36056,206cos2sin xx

45,079,145,079,1 79,145,020

45,079,145,079,1 82,779,145,020

5. a. xxx 5

xxx 52

042 xx 04 xx

0x ; 4xxy 44

Koordinat titik 4,4A

dxxxL 2

1

222

1

32

312

21

xxx

2143

32

dyyyL 2

1

222

1

32

312

21

yyy

214

- 51 -

b.

4

5

2 5xxL 0

4

2 5 dxxxxdx0

4

234

5

23 231

25

31

xxxx

323

642

45361

65

1221

5432

41

6.

Persamaan garis lurus PQ

232

212

21

91

21

xy

21835

25 xy

18115

1835 xy

3

2 210

18115

1835 dx

xxL

3

2

2 1018115

3635

xxx

210

310

18115

37175

365

36180120230175

7. a. 011 2 xx1x ; 1x

jadi 0,1A dan 0,1B

11010 2 yjadi 1,0C

012.111 21 xxxym

0212 22 xxx0123 2 xx

0113 xx

31

x ; 1x

2

131

131

y

2716

94

.34

y

Jadi

2716

,31

M

b. Luas LuasAMCO : OCB

1

0

20

1

2 11:11 dxxxdxxx

1

0

230

1

23 1:1 dxxxxdxxxx

1

0

2340

1

234

234:

234

xxxxxxxx

1

21

31

41

:121

31

41

1212643

:12

12643

5:11125

:1211

8. Misal mxy

xxm 22

022 xxm 012 xmx

0x ;2

1m

x m

y 1

ym 1

dymytL

t0

- 52 -

9.

Luas 2

0

38 dxxA

2

0

4

418

xx

12416

Luas 2

0

3dxxB

441 2

0

4 x

Luas LuasB : 12:4A3:1

10. a. 34 043

042 0 ; 2 ; 2

ambil 2 0karena2.44 x

8Jadi 2 dan 8

b.

2

0

34 dxxxL

2

0

42

412

xx

448

B. Evaluasi Kemampuan Analisis1. a. xxxx 5456 22

01010 2 xx02 xx

01 xx0x ; 1x0y ; 1y

gbr tidak jelas,tolong gbr ulang!!!

1

0

22 5654 dxxxxxL

1

0

2 1010 xx dx

1023 53

10 xx

355

310

b. 1

0

2 54 xxxLI dx

1

0

2 44 xx dx

1023 234 xx

322

34

1

0

2 56 dxxxxLII

1

0

266 dxxx

123 10

32 xx

32:1: LILII

2:3

2. a.

- 53 -

3. L 2

2

24 dxxAEB2

2

3

34

xx

38

838

8

316

16

31

113

64

panjang persegi panjangpanjang AB 422

lebar persegi3

1643

64

panjang

4. gambar & tulisan yang jelas doong!!!

1

0

22 21

22 dxxxL

arc1

3

31

2sin

xx

114

5.

6.


1. a. 3

0

22 dxxV

3

0

24 dxx

3634 3

0

3 x

b.

6

0

2

2dyyV

6

0

2

4dyy

1812

6

0

3

y

2. a. 2

0

22 2 dxxV

3

0

23 44 dxxx2

0

34 434

41

xxx

32

2283

324

b. 2.2.32

22 2V

832

22

32

14

c. 2

0

22 42 dxxV

2023 4xx 2424


- 54 -

3. a. 1

08xV dx

4410

2 x

b. 2

08xV dx

16420

2 x

c. 2

18xV dx

28421

2 x

d. 882

1 xV dx

212 84 xx 4812

e. 2

0816 xV dx

1641620

2 xx

f. 2

1816 xV dx

212416 x 41216

4. a.

2

1

22 dxxV dx2

0

23 4231

xxx

3888

38

b.

1

0

2dxxV

31

31 1

0

3

x

c.

2

2

4dxxV 2

2

5

51

x

564

532

532

d.

1

1

22 316 dxxV

1

1

24 9616 dxxx1

1

35 251

7

xxx

53

9452

14

e.

1

0

432 2 dxxxxV

301

51

21

31 1

0

543

xxx

- 55 -

f.

5

0

44 dxxV

250054 5

0

5

x

g.

1

04xV dx

2210

2 xh.

4

04 xV dx

8214

4

0

2

xx

i.

6

0

4

16dxxV

80

7776801 6

0

5

x

j.

2

0

416256 dxxV

5

20485

162562

0

5

xx

5. a.

2

0

4dxxV

532

51 2

0

5

x

b.

- 56 -

2

0

24 12 dxxxV

15206

32

51 2

0

35

xxx

c.

2

0

6dxxV

7

12871 2

0

7

x

d.

2

1 21 dxx

V

21

2

1

xe.

1

2

4dxxV

531

51 1

2

5

x

f.

2

1 22 1

1 dxx

xV

2

1

3 131

xxx

651

211

31

g.

1

0

41 dxxV

32

31 1

0

3

xx

6. a.

1

0 211 dxx

V

211

1

0

x

b. 1

021 xxV dx

1

0

2

21

34

xxxx

621

341

c. 65

6

2sin4

xV dx

65

6

2cos22

x dx

65

62sin2

xx

3

21

623

21

610

33

4 2

- 57 -


1. a. 3

0

2

91 dyyV

3

0

3

27

yy

213

b. 3

0

2

9dyyV

3

0

3

27y

2. a. 1

0

5

1144 dyydyV

5

1

210 2

144

yyy

1212204

b. 5

114 dyyV

8215

5

1

2

yy

c. 5

11dyyV

821 5

1

2

yy

3. a. 22

0

4

641 dyyV

22

0

5

320

yy

2582

5222

b. 22

0

4

644 dyyV

25

38320

422

0

5

yy

c. 22

0

4

64dyyV

25

2320

22

0

5

y

d. 4

0

4

64dyyV

5

16320

4

0

5

y

e. 4

0

4

644 dy

yV

4

0

5

3204

yy

5

645

1616

4. a. 4

0yV dy

821 4

0

2

y

b. dyyV 5

0

2

3

1253

5

0

3

y

c. dyyV 16

0 4

328

16

0

2

y

d. dyyyV 4

1

2 124

1

23

31

yyy

931521

e. dyyV 50

0 2

6254

50

0

2

y

f. dyyV 0

55

0

5

2 521

yy

2

75252

25

g. 1

0

2

111 dydyyV

102

1

2

212 yyy

23

2

h. dyyV 4

0

4

5

10245

4

0

5

y


- 58 -

5.

a. 4

0

2

169 dxxV

12489

4

0

3

x

b. 3

0

2

91616 dyyV

3

0

3

271616

yx

321648

c.

3

0

2

434 xdyV

322716 3

0

3

y

d.

4

03

43

ydxV

12489 4

0

3

x

6. a. 1

032

dyyV

1

032 yy

b. 2

0

4 dyyV

5

3251 2

0

5

y

c. 2

0yV dy

221 2

0

2

y

d. 1

01dyyV

221 1

0

2

yy


1.

5

2

22 107 dx

xxV

5

2 22 1001449 dx

xxx

5

2

32 10031749

xxxx

9502039147147

2.

1

0

2

1

22

122

dxxxdxxV

2

1

231

0

3

21

1212

xxxx

61

23

127

12

3.

2

1

4

2

2

2

2 14

1 dxx

dxxV

4

23

2

1

23

31

41

41

121

xxxx

19223

1927

12

4. 23

0

246 dxxxV

23

0

32

34

3

xx

29

427

49

41827

5.

1

0

2

1

2

22 4113 dx

xdxxV

1

0

2 69 xx dxx

dx

2

1 416

2

13

10

23

31633

xxx

3

323

146


- 59 -

6. 3

04 yV dy

3

0

2

21

4

yy

215

29

12

7. 2

0

22 410 dxxxxV

2

0

32

355

xx

320

34020

8. a. 2

0

2222 1352 dxxxV

2

0

2424 16925204 dxxxxx

2

0

24 24145 dxxx

3

16024

314 2

0

35

xxx

b.

6

2

22 128 dx

xxV

6

2 22 144

6416 dxx

xx

6

2

23 14464831

xxxx

31217224256256

3208

c. 4

0

2 1684 xxV dx

4

0

2 16646416 xxx dx

4

0

2 643216 dxxx

3

160064163

16 4

0

23

xxx

d. 1

0

2

1

22222 dxxxdxxV

2

1

2310

2 4534

xxxx

3

324153

28

9. 1

0

4 dxxxV

103

51

21

1

0

52

xx

10. 2

2

42 124 dxxxV

2

2

53 351

32

xxx

1574

26528

238

11. 2

0

224 dxxxV

2

0

32

34

xxx

3

203848

12. a

ady

ay

aV2

2

4

22

16

a

aa

yya

2

22

52

80

333

516

54

4 aaa

13. 5

1 2100 dxx

V

80100 5

1

x

14. 2

1

42 44 dxxxxV 2

1

523

51

4231

xxxx

15

182531

4637

15. 4

1

432 12284816 dxyyyyV 4

1

5432

513

3282416

yyyyy

32486205765

3182036080


1. a. 4

0

364 xV 8yd

19241

644

0

4

xx

b. 8

034

16 yV 4xd

7

51273164

8

0

37

yy

- 60 -

c. 8

034

yV 4xd

7

38473 8

0

37

y

d. 4

0

3xV 8yd

6441 4

0

4

y

2.

0

2

2

0

22

24

24 dxxxdxxxV

0

2

22 444

xdx

444

22

0

2 xdx

2

0

220

2

22 421

44

21

4

xx

484

84

3.

4. 2

0

2 64162 dxxxV

4

2

22 1616464162 dxxxxx

4232

0

23 322648312 xxxxx

312136456212832

382

5. 3

4

2sec

xV dx

13tan 3

4

x

6. 4

0

2sec

xV dx

40tan x

7. a. 4

0

22 sincos

xxV dx

22sin

21 4

0

x

b. 4

0

22 cossin2sincos

xxxxV dx

21

42cos

21 4

0

xx

A. Pilihan Ganda

1. C. 0

221 dxxxx

2. A.421

30

1

4560

1

5 101051 xxxxdxxx

xx 25 dx0

1

234567

21

35

25

265

71

xxxxxx

421

21

35

25

265

71

3.

5

5 2

5

14x

x

4. E.5

5y

2

2

434sin dxxxxx

2

2

432

2cos21

21

dxxxxx

xxxx 4cos

21

21

41

2cos21

412

2

dxxx 43

xxxx 4cos81

81

2cos21

412

2

dxxx 43

Uji Kompetensi AkhirBAB I

- 61 -

xxxxx81

2cos81

2sin41

81 2

2

2

54

51

41

4sin321

xxx

554

564

21

000

5. A. cxxx 21cos8

21sin4

xx21cos2 cxxxdx

21cos8

21sin4

x2 x21cos

2 x21sin2

0 x21cos4

6. C.38

2

0

2 2xxL 2

3

2 2xxdx dx2

3

232

0

23

31

31

xxxx

38

53

194

38

7. B. 5210 satuan volume

2

1

42 44 dxxxxV 2

1

523

5142

31

xxxx

5210

5331263

8. C. 0

2

0

22 cossin

xx dx

2

02cos

x 02sin21 2

0

xdx

9. D. xx 4sin812sin

41

xx 3sinsin xxdx 4cos21

2cos21

dx

cxx 4sin81

2sin41

10.

7363 2712 xxdxxx

982 250462

563 xxxx

1025040

6 x

6

43

223

22

040.56

2504

6

2563

271

xxxx

xxxx

62040.51

x

lanjutannya manaa !!!

3x 62 x23x 77

1 2 x

x6 8561 2 x

6 95041 2 x

0 10040.51 2 x

11. A. cxxxx 753 sin71

sin53

sinsin

x7cos xxdx cossin132 dx

xxxx cossinsin3sin31 642 dx

xcos xdx 2sin3 xd sin

x4sin3 xxd 6sinsin xd sin

cxxxx 753 sin71

sin53

sinsin

12. D.651

3

2

2 312 dxxxxL3

2

23 221

31

xxx

6512

25

319

- 62 -

13. C. 1,2

k

odxxkxL 288,02

288,031

232

k

o

xxk

2888,0632

333

kkk

2,1k

14. E. 61

dxxx

dxx

V 144

2

1

21

0

2

2

1

231

0

3

21

121

121

xxxx

61

23

127

2

15. lanjutannya manaaa!!!

xxdx

3


3

0sincos

ttfxxf dt

3

0sin

ttf xxfdt cos

17. C.21

1

1

1

1

32

31

21

1

axxx

adxxax

1231

232

aa

21

a


dxx

xxx 23

231

2233

231

2222

33

2231

31

2233

2233

6

3322 2233

19. B. 238

21

21

2 12 dxxx

21

21

23

3

xxx

3

226231226231

212122212221

23822242

310

20. D.1221

0

1

23 2xxxL dx xxx 222

1

3 dx2

0

2240

1

234

31

41

31

41

xxxxxx

1221

434

4131

41

- 63 -

21. B. satuan6

343 luas

8

1

2 89 dyyyL8

1

23

829

3

yyy

634356

2567

3511

22. B. satuan3548

volume

3

3

4269 dxxxV

3

3

53

51

29

xxx

5

3483

518

312318

23. Lanjutannya manaaa!!!

dx

xx

x3

3 1


dxxx

x3

3 1


dx

xx

2

tan1tan

xx 22 cos2tan dx

B. Evaluasi Kemampuan Analisis1.

2. 1

0

2 0cdxcbxax

1

0

23 0cexbecdxaebdadx

0234

1

0

23

cexx

becdx

aebdad

0234

cebecdaebdad

012

1266443

cebecdaebdad

01266443 cebecdaebdad

- 64 -

3.

4. a. xx cossin dx

lanjutannya mana booo!!!

b. xx cos

1

sin

1dx

5. 2

1

4

2 2

141

41

dxx

dxxL

4

2

2

1

2 141

81

x

xx

satuan83

21

41

41

83

luas

kunci sukino 3a bab 1

Education