Page 41 - Kalkulus Lanjut

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

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

4 1 2
= ∫ ( + )
2
3
2 3 1
4
7
= ∫ ( + 3 )
2
2 3
4


 7 y + y 3 
=
 3 2 
 7

=

 2
 4 + 4 3  −  7 + 2 3 

 3
 3

2
= 60
3

4 2 4  2 
2
2
 (

3.   ( xy + 3 y ) dydx =   xy + 3 y ) dy dx
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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