Math 152 Exam 1 Review

1. Find the area of the region bounded by:

a)

b)

2. Find the volume of each solid.

a) The base in the x-y plane is an isosceles triangle with base 6 m on the x-axis and height 4 m on the y-axis. Cross sections perpendicular to the y-axis are semicircles.

b) Same as a except cross sections perpendicular to the x-axis are semicircles.

3. Find the volume of each solid:

a) The region bounded by y = ln(x) and y = x for x between 1 and 2 is rotated about the x axis.

b) The same region as in a is rotated around the line y = - 3.

c) The same region is rotated around the y-axis.

d) The same region is rotated around the line x= - 3.

4. Find the volume if the region bounded by , is rotated about the line y = 5.

5. The work required to stretch a spring from 10 cm beyond its natural length to 20cm beyond its natural length is 3 J. Find the work required to stretch it from 15 cm beyond its natural length to 25 cm beyond its natural length.

6. A rope is 30 ft. long and weighs 60 lbs. It hangs from a 50 ft. tall building. Find the work done in pulling 8 ft. of the rope to the top of the building.

7. A semispherical tank has a spout 1 m above the top. The radius of the tank is 6 m. The tank is full of water. a) How much work is done in pumping all the water out the spout?

b) How much work is done by gravity if all the water leaks out a hole in the bottom.

8. Find each integral.

b) c) d)

e) f) g) h)

9. Evaluate the definite integral or find the indefinite integral.

a) b) c)

d) e) f)

g)