NAME
MATH 106 PRACTICE
MIDTERM 2
Please
work out each of the given problems. Credit
will be based on the steps that you show towards the final answer.
Show your work.
PROBLEM 1 Set up the
integrals that solve the following problems.
Sketch the appropriate diagram for each. Then use a calculator to finish the problem.
A) (10
Points) Find the volume of the solid that is formed by revolving the region
bounded by y = x3 + x and y
= x2 + x
around the y-axis.
Solution
B)
(10 Points). Find the volume of the solid that is formed by
revolving the region bounded by y = x4
and y
= x
between x = 0 and x
= 1/2
about the line
y = -10.
Solution
C) (10
Points) Find the volume of the solid that is formed by revolving the region
bounded by y = x3 - x
and y = 3x around the line x
= 5.
Solution
D) (10
Points) Find the area of the region bounded by the curves
y =
x3 - 3x2 - 9x + 12 and y
= x + 12
Solution
E)
(10 Points) Find the length of the curve y
= sin x
for 0 < x < 2p.
Solution
F)
(10 Points) Find the volume of the sphere of radius
2.
Solution
PROBLEM 2 .
A) (10
Points)
Find the derivative of
sec-1(2x + 1)
Solution
B)
(10 Points) Show that
PROBLEM 3 Find the following indefinite integrals
A) (15
Points)
Solution
B)
(15 Points)
Solution
Problem 4 (20 Points)
When completed, the
International Space Station orbiting at 238 miles above the surface of the earth
will weigh one million pounds (at the surface of the earth 4000 miles from the
center). How much total work will
it take to send the entire station in orbit?
Solution
Problem 5 (20 Points)
A
30 foot chain that weighs 3
pounds per foot is used to lift a 200 pound piece of sheet metal from the ground
to the top of a 30 foot tall building. How
much work is required?
Solution