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Unformatted text preview: , , 1). 9. (a) Let x/ 2 = u and y/ 3 = v , solve for u and v to get the transformation T ( u, v ) = (2 u, 3 v ). ZZ S (2 u + 3 v )6 du dv where S is the unit disk. Now use polar coordinates to get 6 Z 2 π Z 1 (2 r cos θ + 3 r sin θ ) r dr dθ = 0 (b) Let T ( u, v ) = ( uv, 2 uv ). Since u = yx , we get 0 ≤ u ≤ 2. Since v = y2 x , we get1 ≤ v ≤ 0. Compute ∂ ( x, y ) ∂ ( u, v ) = 1. Z 2 Z1 u 2 dv du = 8 / 3 2...
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 Fall '12
 IlyaKofman
 Math, Calculus, dy dx, dr dθ, dρ dθ dφ

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