Practice+Test+5 - 0.8 m to a length of 0.75 m Find the work...

1
Practice Test 5
Evaluate the integral
1.
∫
- dy y y
2
) 2 (
2.
dx
x
x x
∫
-
7
9 5 8
3.
∫
dx x x ) (sin sec cos
2
4.
∫
- -
-
dx
x x
x x
4 3
2
2 3
2
5.
dx e x x x
∫
-
- + +
1
1
6 5
2
) 5 2 (
6.
∫
-
21
14
5 dx x x
7.
∫
3
0
4
tan sec
π
dx x x
8. Make a sketch of the region bounded by y = x
2
and y = 4x (or x = y
2
and x – y -2 = 0) and find
the area of that region.
9. Calculate the volume of the solid generated by revolving the region bounded by y = x 2 and
y = 4 – x 2 about the x-axis (or x = y 2 and x – y -2 = 0 about the y-axis)
10. Calculate the volume of the solid generated by revolving the region bounded by y = x 2 -5x
and y = 0 about the y-axis (or x
2
= 4y and y = 0 about x –axis) .
11. Set up the integral to solve: A force of 25N is required to compress a spring of natural length