Let (a) Show that the mapping u = xy, v = x y maps D to

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Let I = (x - y) dx dy, where

D = {(x, y): 2  xy  4,0 < x-y 3, x  0, y  0}

(a) Show that the mapping u = xy, v = x − y maps D to the rectangle R = [2, 4] × [0, 3].
(b) Compute ∂(x, y)/∂(u, v) by first computing ∂(u, v)/∂(x, y).
(c) Use the Change of Variables Formula to show that I is equal to the integral of f (u, v) = v over R and evaluate.

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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