Math 152 In Class Exam 1 Review J. Lewis

1. Find the area of the region bounded by

a)

b)

2. Find the volume of an object which has a triangular base with vertices (0,0), (0,4),and (6,0) and

a) cross sections perpendicular to the x- axis are squares.

b) cross sections perpendicular to the y- axis are semicircles.

3. The region bounded by is rotated around the x-axis. Set up the integral to find the volume using

a) washers.

b) cylindrical shells.

4. Find the volume of the solid formed when the region bounded by is rotated around

a) y = -1

b) y = 4

c) x = 5

5. A spring has a natural length of 10 cm. The force needed to hold it at 15 cm is 2 J.

Find the work done in stretching it from 20 cm to 30 cm.

6. A rope is 50 ft ling and weighs 75 lbs. The rope hangs over a tall building.

a) Find the work done in pulling 10 ft of the rope to the top.

b) Find the work done in pulling the whole rope and a 100 lb weight to the top.

7. Find the work done in pumping the water out of the outlet for the given tank.

a) A trough is full of water. The trough is 6 m wide at the top, 4 m high and 12 m long. The outlet is at the top of the tank.

b) A semispherical tank has a radius of 5 m and is full of water. The outlet is 2 m above the top of the tank.

c) A spherical tank has a radius of 3 m and the water is 5 m deep. The spout is 1 m above the top of the tank.

8. Find each integral.