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midterm1asol

# midterm1asol - Math 32B Spring 2010 Midterm 1 Name Student...

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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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