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Soal 1.

Penyelesaian analitis :

Hitunglah y pada saat x = 5

Jawaban : Jika diintegralkan menjadi:

(3y - 5) (1+X2)3/2 - 2*(2)^1/2 =

dy/d! = 5! - 3!y

1 + !2

"#al$eak

y ! %(!)

&et#de '' 1,3. 5 -1223'-13

0= 5

r ! y dy/d!=% (!y)

1 2 -5

1 15 15 -1153.,15 naliti4 1,3.2.

2 2 1,23. -3,23.

3 25 1,,23 -1,1, Jadi y(5)= 1,,32,31

3 1,1,1. -5,233

5 35 1,,3 -215.51

, 1,,.311 -11,,32 "alat 3.15

5 1,,31 -,5.5

. 5 1,,33 -1..25

&et#de 6"' 78tta

9' 1 9' 2

0 = 5

r Xr ;r dy/d!=% (!y) 0 =

1 2 -5

1 15 15 -1153.,15 r

2 2 1,23. -3,23.

3 25 1,,23 -1,1, 1

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3 1,1,1. -5,233 2

5 35 1,,3 -215.51 3

, 1,,.311 -11,,32

5 1,,31 -,5.5 5

. 5 1,,33 -1..25 ,

.

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9' 3

5

Xr 71 72 ;r

1 2 0 = 5

15 -25 -12,231 123.5

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2 2511. -231 15.2. r Xr

25 553 -3 ,..1 1

3 55.3 -2 .,, 1 15

35 53. -12 225, 2 2

5,3 -2,.1 113. 3 25

5 55252 -3225 -.. 3

5 5552 -3,13 -23, 5 35

,

5

. 5

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9'

0 = 2

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71 72 73 ;r r Xr 71

2

-25 1112.5 -25532 235, 1 1,23.

-.33 2252 -3,5,3 312,, 2 33.,15

-...3, 313 -.5,122 3.. 3 5,23

-13,,1 -5.5. 5.215 ,,231

-1.,.. 325., -,,5., ,.112 5 .,153.

-23.33 553. -3.11 ..5,

-23 ,5,,.. -.1151 12233 "< = >?/@

-31. 3,11,5 -.3321 153.5

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72 73 7 ;r

1

1

1

1

1

1

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JAB6

6eraCa 7#mD#nen =

= E * Fa% - G * FaD + ? * (-ra)

E * Fa%2 3 m#l

min m3

, m#l/min

G = dCa/dt = , -2 Fa - Fa2

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1 m3

1

Fa2