Thomas Calculus 13th [Solutions]

492 Chapter 6 Applications of Definite Integrals
CHAPTER 6
PRACTICE EXERCISES
1.
2.
3.
2 2
A( x) (diameter) x x
4 4
4
2 4
x 2 x x x ; a 0, b 1
b
1 5/2 4
V A( x) dx x 2x x dx
a
4 0
2 5 1
x 4 7/2
x x 1 4 1
4 2 7 5
0
4 2 7 5
(35 40 14)
9
4 70 280
2 3
2
A( x) 1
(side) sin 2 x x
2 3 4
3
4
2
4x 4 x x x ; a 0, b 4
b
3 4 3/2 2
V A( x) dx 4x 4x x dx
a
4 0
3 4
3 2 8 5/2
3
2x
x x
32
8 32 64
4 5 3
0
4 5 3
32 3 8 2 8 3 8 3
1 (15 24 10)
4 5 3 15 15
2 2
A( x) (diameter) (2sin x 2cos x)
4 4
4
2 x x x 2
x x
4 sin 2sin cos cos (1 sin 2 );
5
b
,
4 4
a
5 /4
(1 sin 2 cos 2
5 /4
x ) dx x x
/4 2 /4
a b V A( x)
dx
5x
2 2
5
cos cos 2
4 2 4 2
2
4.
2
2
2
4
3/2 2
A( x) (edge) 6 x 0 6 x 36 24 6 x 36x 4 6 x x ; a 0, b 6 V
b
6 3/2 2 2 3/2 2 2 5/2
A ( x ) dx
0 36 24 6 x 36 x 4 6 x x dx 36 x 24 6 x
3 18 x 4 6 x x
a 5 3
0
3
2 8 2 6 1728 1728 1800 1728 72
5 3 5 5 5 5
216 16 6 6 6 18 6 6 6 6 216 576 648 72 360
3 6
5.
2 2
2 5/2
4
x
x
4 4 4 4 16
A( x) (diameter) 2 x 4 x x ; a 0, b 4 V A( x)
dx
4 5/2 2 7/2
4x x x dx 2x 2 x x
32 32
8 2
32
32
1
8 2
4 0 16 4 7 516
0
4 7 5 4 7 5
8
(35 40 14)
72
35 35
4 5 4
b
a
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