Thomas Calculus 13th [Solutions]

358 Chapter 5 Integration
33.
3
3 3
7
7
x 2
dx
7
0
3 3
34.
0.3 2 (0.3)
s d s
3
0
3
0.009
35.
1
3
2
1/2
t 2
dt 1
36.
0
3 24
0
/2 3
2 2
3
d
3 24
37.
2 a 2
(2 a) 2 2
a 3a
a x dx 2 2 2
38.
a
2
3a
3a
2
2
x dx
a
2 2
a
39.
3
b 2
x
0
dx
3
3
b
b
3 3
40.
3 b 2 (3 b) 3 3
x dx 9b
0
3
41.
43.
1
7 7(1 3) 14
3 dx 42. 2 2
5 x dx 5 x dx
0 0
2 1 2
2 2
2 0
0 (2 t 3) dt 2 t dt
1 0
3 dt 2 2 2
3(2 0) 4 6 2
2
5 2 0 10
2 2
2
44.
2 2
t 2 dt t dt
0 0
2
0
2
2 2
2 dt
0 2 2 0 1 2 1
2 2
45.
1
2 1
z
2
dz
1 1
2 1 dz z dz
2 2
1
1
2
2 1 dz 2 1
z dz
2 2
1[1 2] 1 2 1 1 1 3 7
2 2 2 2 2 4
46.
47.
0 0 0 3 0
2 2
3 0
3 (2 z 3) dz
3 2 z dz
3 3 dz 2 z dz
0 3
3 dz 2 2 2
3[0 3] 9 9 0
2 2 2 2 2 2 1 2
3 3 3 3
3 3
2 0 1 0 2 1 7
1 3 u du 3 u du
1 3 u du u du
0 0
3 3 3 3 3 3 3 3 3 3
7
48.
1 2 1 2 1 2 1/2 2
3
1
1/2 24 u du 24 u du
1/2 24 u du u du
0 0
24 3 3 24 3
7
1
3
2
7
8
49.
2 2 2 2 2 2
3 3 2 2
2 0 2 0
0 (3 x x 5) dx 3 x dx x dx
0 0 0
5 dx 3 3 3 2 2
5[2 0] (8 2) 10 0
50.
0 2 1 2 1 2 1 1
3 3 2 2
1 0 1 0
1 x x 5) dx
0 x x 5) dx 3 x dx x dx
0 0 0
dx 3 3 3 2 2
5(1 0)
3 5 7
2 2
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