Thomas Calculus 13th [Solutions]

1102 Chapter 15 Multiple Integrals
12.
1 x
4 x
1 dy dx 1 dy dx
0 x
1 x 2
1 4
0 y x
x
x
dx 1
y x 2
dx
1 4
x x dx x x 2 dx
0 1
3/2 2
1
3/2 2
4
2 x 1 x 2 x 1 x 2x
13
3 2 0 3 2 1 3
13.
6 2 y 6 2 3
2
2 dx dy 2y y dy y
y
0 y /3 0 3 9
36 216 12
9
6
0
14.
2 3
3 2x x
3 2 3 2 1 3
dy dx 3x x dx x x
0 x
0 2 3 0
27 9 9
2 2
15.
/4 cos x
dy dx
0 sin x
/4 /4
(cos x sin x) dx sin x cos x
0
0
2 2
(0 1) 2 1
2 2
16. 2 y 2 2 2
2 dx dy y 2 y dy
1 y
1
2 3 2
y y
2y
2 4 8 1 2 1
2 3 3 2 3
1
5 1 9
2 2
17.
0 1 x 2 1 x
dy dx dy dx
1 2x
0 x/2
0 2
1 (1 x ) dx
0
1 x dx
2
2 0 2 2
x x x x 1 1 (2 1) 3
2
1
4
0
2 2
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