MATH 221 Test #3 Name________________
Instructions: Answer all the questions on the paper
provided and show all your work so that partial credit may be given. You may use a calculator on all questions.
1. Show that 
by using a
substitution and by differentiating. (15)
2. Find 
(10)
3.
Find
f(x) given that 
and f(-1) = 2. (10)
4. Find the area of the region enclosed by 
and 
. (15)
5. A farmer has 6000 feet of fencing and wishes
to construct a pasture as pictured below.
Find the maximum area of such a pasture. (20)
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6.
In
the graph below 
. Find each of the
quantities listed below and write the integral that is needed to find that
quantity. (30)
a)
The
area of R2.
b)
The
volume of the solid obtained if R1 is rotated about the x-axis.
c)
The
volume of the solid obtained if R3 is rotated about the y-axis.
