Thomas Calculus 13th [Solutions]

Section 15.4 Double Integrals in Polar Form 1107
1 3y
24.
2
1/2 1
0
3/2
y
x dx dy or
1 3 1
2 x dy dx
x dy dx
1 x
3/2 x/ 3
25.
2 x y
2 x
2 y
2 dy dx or
0 0
2 2
y 2
x 2
y 2
0 y
dx dy
26.
3 4 2 2
3
0 0 x y dy dx or 4 3 2 2
3
x y dx dy
0 0
27.
/2 2 2 sin 2 /2
r dr d
0 0 0
2 (2 sin 2 ) d 2( 1)
28.
/2 1 cos /2 2
A 2 r dr d 2cos cos d 8
0 1 0
4
29.
/6 12cos3 /6 2
A r dr d d
0 0 0
2 144 cos 3 12
30.
2 4 /3
8
2 2
A r dr d d 64
0 0 9 0
27
3
31.
/2 1 sin /2
A r dr d 1 3 cos 2 d 3
0 0 2 0 2 2 8
2sin 1
32.
/2 1 cos /2
A r dr d 3 cos 2 d 3
0 0 0 2 2 2
4 2 2cos 4
4 /2 a 2 2 4
/2 3 2a
a 0 0 3 a 0
3
33. average r a r dr d a d
2 2
4 /2 a 2 4
/2 3 2a
a 0 0 3 a 0
3
34. average r dr d a d
2 2
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