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Unformatted text preview: Math 213  Quiz 8
Name Solution
1. We define the improper integral (over the entire plane R2 ) by I=
R2 e(x 2 +y 2 ) dA = lim a e(x
Da 2 +y 2 ) dA where Da is the disk of radius a and center the origin. Show that I = . Using polar coordinates, e(x
Da
2 +y 2 ) a 2 0 dA =
0 a er r d dr 2rer dr
0 a2
2 2 = =
0 eu du
2 = ea + . Since ea 0 as a , it follows that I = .
2 ...
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This note was uploaded on 05/09/2008 for the course MATH 2130 taught by Professor Dorais during the Spring '08 term at Cornell University (Engineering School).
 Spring '08
 DORAIS
 Math, Calculus

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