Exam 1
M175004
Spring, 2004
Name:
(1 pt.)
•
Show all your work.
•
If you use your calculator to do anything beyond arithmetic or graphing, be sure to indicate
“Here I used my calculator” somehow.
•
If a problem says “Write an integral for...,” you must express everything in terms of your
variable of integration.
•
If you compute an integral, show your work and don’t skip any big steps. I have to know that
you
did it, not your calculator.
1. (10 pts.) Let
R
be the region enclosed by the curves
y
= 1

x
3
,
y
= 0
,
x
= 0
(a) Chose an axis of integration.
(b) Draw a typical slice of area.
(c) Compute the area of that slice.
(d) Write an integral for the total area of
R
.
2. (15 pts.) Suppose that the region from Problem 1 is a sheet of material with variable density:
ρ
= (
x
+ 1) g/cm
2
. The axes are measured in cm. Find the total mass.
•
You ARE allowed to reuse anything from Problem 1 without showing work.
•
You are NOT allowed to use your calculator to evaluate the integral. Do it yourself and
show all the steps.
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 Calculus

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