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Unformatted text preview: Math 213 -- Quiz 8
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
2 +y 2 ) a 2 0 dA =
0 a e-r r d dr 2re-r dr
2 2 = =
0 e-u du
2 = -e-a + . Since e-a 0 as a , it follows that I = .
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