Instructions: DO NOT TURN IN. This is practice for the midterm. I will base some of the midterm
problems on some of the problems here.
1Stewart, section 7.7: #5, 9, 10, 13, 30, 32, 35, 39
2Stewart, section 7.8: #1, 3, 7, 9, 13, 19, 27, 30, 31, 64, 69, 70
3The portion of the graph of y= tan−1xbetween x= 0
and x= 1 is rotated around the y-axis to form a container.
The container is filled with water. Use n= 6 subdivisions and
Simpson’s Rule to approximate the work required to pump all
the water out over the side. Distance is measured in meters and
the density of water is 1000 kg/m3.
x
y
1
4The rocket in Problem 3 of Week 4 required the following force when the rocket was at a
distance of xfrom the center of the moon:
F(x) = R2P
x2pounds.
a) The total amount of work done raising the payload from the surface (an altitude of 0, so x=R)
to an altitude of R(x= 2R) is
W=Zb
a
F(x)dx =Z2R
R
R2P
x2dx = mile-pounds.
b) How much work will be needed to raise the payload from the surface of the moon to the “end of
the universe”?