Thomas Calculus 13th [Solutions]

Chapter 5 Practice Exercises 409
10. (a)
(b)
(c)
(d)
(e)
2
1
2
g x dx g x dx 1
0 7 0
7
( ) 7 ( ) (7) 1
2 2 1
g x dx g x dx g x dx
1 0 0
( ) ( ) ( ) 1 2 1
0 2
f ( x) dx f ( x)
dx
2 0
2 2
f x dx f x dx
0 0
2 ( ) 2 ( ) 2( ) 2
2 2 2
g x f x dx g x dx f x dx
0 0 0
[ ( ) 3 ( )] ( ) 3 ( ) 1 3
11.
12.
13.
2
x 4x 3 0 ( x 3)( x 1) 0 x 3 or x 1;
Area
1 2 3 2
( x 4x 3) dx ( x 4x 3) dx
0 1
3 1 3
3
x 2 2
2x 3x x 2x 3x
3
0
3
1
1 3 2
2(1) 3(1) 0
3
3 3
3 2 1 2
2(3 ) 3(3) 2(1) 3(1)
3 3
1 1 0 1 1 8
3 3 3
2
2
x
x x
1
4
0 4 0 2;
Area
2 2 3 2
1 x
dx 1 x
2 4 2 4
dx
x
3 2 3 3
x
x
x
12
2
12
2
2
3 3
( 2) 3
3
2 2 3 3 2 2
12 12 12 12
4 4 3 4 13
3 3 4 3 4
5
2/3
5x 0 1
2/3
x 0 x 1;
Area
1 2/3 8 2/3
(5 5 x ) dx (5 5 x ) dx
1 1
5x 5/3
1
5/3
8
3x 5x 3x
1 1
5/3 5/3
5(1) 3(1) 5( 1) 3( 1)
5(8)
5/3
3(8) 5(1)
5/3
3(1)
[2 ( 2)] [(40 96) 2] 62
14. 1 x 0 x 1;
Area
1 4
(1 x) dx (1 x)
dx
0 1
x 3/2
1
3/2
4
2 2
3 x x 0 3
x
1
2 3/2 2 3/2 2 3/2
1 (1) 0 4 (4) 1 (1)
3 3 3
1
4
16 1
2
3 3 3
Copyright
2014 Pearson Education, Inc.