Thomas Calculus 13th [Solutions]

Chapter 15 Practice Exercises 1143
6.
1 y
1
2 3/2
y
x dx dy x dy
0 y
0 3 y
1 3/4 3/2 7/4 5/2
1
2 y y dy 2 4 y 2 y
3 0 3 7 5 0
2 4 2 4
3 7 5 35
1 x
1 1/2
2 x dy dx x
0 x
0
x x 2
dx
1 3/2 5/2
0 x x dx 5/2 7/2
1
2 x 2 x 2 2 4
5 7 0 5 7 35
7.
2 2 (1/2) 9
3 (1/2) 9 x
3 y
y dy dx
3 0 3 2
0
3
1 2 9
3 8 9 x dx x x
8 24
3
3 3
x
2
dx
27 27 27 27 27 9
8 24 8 24 6 2
2
3/2 9 4 y
y dx dy
3/2
2y 9
2
4y dy
9 4 y
3/2
3/2
1 2 2 3/2
9 4y
1
9
27 9
4 3 6 6 2
0
0 2
0
8.
2 2
2 4 x
2 4 x
2x dy dx 2xy dx
0 0 0 0
2 2 2 3
2x 4 x dx 8x 2x dx
0 0
4 2
2
x x
16
2
0
2
4 16 8
4 4 y
4 2
4 y
2x dx dy x dy
0 0 0 0
4
0
2 4
y
16
2
0
2
(4 y ) dy 4 y 16 8
9.
1 2 2 /2 2
2
2 2 2 2
x dx dy x x dy dx x x dx x
0 2y
0 0 0 0
4cos 4cos 2 cos sin sin 4
10.
2 1 x 1 2x
x 1 x x
e dx dy e dy dx xe dx e e
0 y/2 0 0 0
0
2 2 2 2 1
2 1
11.
3 3
8 2
1
2 y
1 1
2 4 y ln17
3
dy dx dx dy dy
0 x
4
0 0
4 4 0
4
y 1 y 1 y 1 4
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