Math 32B, Spring 2010, Midterm 1
April 21, 2010
Name:
Student #:
Section:
There are six problems. You have 50 minutes. Do as many problems as you can in
this time, skip those which you cannot solve. Each problem is worth 5 points. You
are not allowed to use calculators. For most of the problems it is a very good idea to
draw a picture of the domain of integration.
..........
Good luck!
01————02————03————04————05————06————
Total points:
Grade:
1
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Problem 1
Consider a thin plate shaped like the half annulus described in polar
coordinates by 10
≤
r
≤
50 and 0
≤
θ
≤
π
. Suppose the thickness
d
of
the plate varies somewhat and has been measured at four points given
in the following table (locations in polar coordinates):
r
θ
h
20
π/
4
1
40
π/
4
2
20
3
π/
4
2
40
3
π/
4
4
Give a reasonable approximation for the volume of the thin plate
using a midpoint Riemann sum in polar coordinates. Give the answer
as a multiple of
π
, do not insert a numerical value for
π
.
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 Winter '10
 Corbin
 Polar Coordinates, Polar coordinate system, dx, creative solution

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