Page 39 - Bahan Ajar Kalkulus Lanjut

1 2 1 2 1 1
2
1. ∫ ∫ = ∫ (∫ ) = ∫ ( ) = ∫ (2 − 1) = 1
0 1 0 1 0 1 0

4
2
4
2
2
2
2
2. ∫ ∫ ( + ) = ∫ (∫ ( + ) )
2
2 1 2 1

4 1 2
= ∫ ( + )
3
2
2 3 1
4
7
= ∫ ( + 3 )
2
2 3



 7 y + y 3  4
=
 3 2 
 7   7 
=
 4 + 4 3  −  2 + 2 3 
 3 2   3 
= 60 3

4 2 4  2 
2
3.   ( xy + 3 y ) dydx =   xy + 3 y ) dy dx
2
 (

2 1 2  1 
4  xy 2 3  2


=  + y  dx
2  2 1 
4 2
4  x 2 . 2   x 1 . 2   x 3 

=  + 2 3  −  +1 3  dx =   2 + 7 dx





2  2   2  2 1
4
 x
=  3 2 + 7  x 
4
  2
=
) ( +
(12 + 28 − 3 14 )

= 23

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