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Unformatted text preview: 2 e v ± ± ± v =1 v =1 du = ee1 3 Z 4 1 u 2 du = 7( ee1 ) . 4. First we use cylindrical coordinates to integrate RRR B e z dV : Z 11 Z 2 π Z √ 1z 2 e z r dr dθ dz = Z 11 Z 2 π e z 1z 2 2 dθ dz = π Z 11 e z (1z 2 ) dz = π ² e z ± ± 11( z 2 e z ) ± ± 11 + Z 11 2 ze z dz ³ = π ² ( ee1 )( ee1 ) + (2 ze z ) ± ± 11Z 11 2 e z dz ³ = π ´ 2 ( e + e1 )2 ( ee1 )µ = 4 e1 π. Volume of the unit ball B is 4 π/ 3 (or it can be computed as R 11 R 2 π R √ 1z 2 r dr dθ dz = R 11 π (1z 2 ) dz = 4 π 3 .) Hence the required answer is 4 e1 π 4 π 3 = 3 e1 . 1...
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 Spring '11
 wang
 Calculus, Multivariable Calculus, dz dy dx, dz dx dy, dy dz dx

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