Homework 3-due February 12th
You only have to hand in homework problems 1, 2 and 3. The practice problems are optional.
Homework Problems
1. A tank full of water has the shape obtained by revolving the curve y = arcsin(x) around the y axis
from x = 0 to x = 1. Find the work required to pump the water out of the tank. (The density of water
kg
is 1000 m
3 ).
2. A tank full of water has the shape obtained by revolving the parabola, y = x2 around the y axis from
kg
x=2 to x=4. Find the work required to pump the water out of the tank. (The density of water is m
3 ).
R2
3. Let f (x) be a two times differentiable function such that 0 x2 f 00 (x) dx = 2.
R2
If f 0 (2) = 1 and f (2) = 2, find the 0 f (x) dx. Hint: use integration by parts and
don’t be scared of the fact that you don’t have a formula for f (x).
Practice Problems. Solve the following problems from the textbook (7th edition).
1. 13-26, page 450.
2. 19-26, page 454.
3. 68-70, 72, page 470.
1