250481362-Pembahasan-Fismat-Boas.docx

Section 2 Chapter 5

1.

  ∫= ∫= 3  

 Jawab :

  ∫= ∫= 3     = (∫ 3  ) ( ∫  )  = (  x │  ) ( y│ )  2

 

=  . (4-2) = 3 2.

  8   ∫=− ∫=

 Jawab :

  8   ∫=− ∫=   = (∫ 8  ) ( ∫−   )   = (  x │  ) (  y │ − )    16  4 )   2  = ( 16 2

2

= 12 . -3/2 = -18

3.

  ∫= ∫=  

 Jawab :

  ∫= ∫=     = ∫=  (∫=  )    = ∫= ( x│ ) dy  42) = ∫=(42) = ( 4y –  y  y │ ) 2

=4

4.

 / ∫= ∫=    

 Jawab :

 / ∫= ∫=    

 /  (∫=    )   ∫=   / = ∫= (  x │  ) dx    = ∫= (  x  ) dx    = (  x │ )  =

2 2

3

= 2,6 5.

  ∫= ∫=    

 Jawab :

  ∫= ∫=       = ∫=( ∫=    )    = ∫= (  y2 │  ) dx    2x  2 = ∫= ( e  –   x  ) dx   2x 3 = ½ ( e  /2 –  x  /3 ) │ 

= 1/4 ( e2-e0 )- 1/6 (1 -0 ) = e2 /4 -5/12

4.

  ∫= ∫= √      Jawab :

  ∫= ∫= √       = ∫=  (∫=√    )      = ∫= (  x │ √ ) dy     = ∫= (  y -  y) dy     = (  y -  y │ )   2

4

5

2

= (3,2 –  1) –  ( 0,1-0,25 ) = 2,35 5.

∬A (2x3y)dy dx, where A is triangle with vertices (0,0) , (2,1) , (2,0)  Jawab :

 /( ∫= ∫= 23)   / = ∫=( ∫=(23)) 

 ( 2    │/ )dx ∫=  = ∫=  - 3/8 x  dx  = ∫= 5 /8 x  dx = ( 5/24 x │  ) 2

=

2

2

2

3

= 5/3

9.

∬   , where A is the area shown in Figure 2.8  Jawab :

  ∫= ∫= / sin     = ∫=( ∫= / sin  )    )  = ∫=(  cos  │ /  = ∫=( 1 0 )  = ∫= 1  = ( y │  ) = 4 –  2 =2 10.

∬   , where A is the area shown in Figure 2.8  Jawab :

  ∫= ∫= /      = ∫=( ∫= /   )    )  = ∫=( xy │ /   = ∫=          = ∫=(  )   = ( ¼  y │  ) = 4   = 3  2