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xy = 1, xy = 9, xy = 1, xy = 25 in the first quadrant of the xy-plane. (a) Graph the region D. (b)
xy = 1, xy = 9, xy = 1, xy = 25 in the first quadrant of the xy-plane. (a) Graph the region D. (b) Using the non-linear change of variables u = xy and u = xy, find x and y as functions of u and v. x = x(u, U) = y = y(u, U) = (c) Find the determinant of the Jacobian for this change of variables. o(x, y) = det a(u, U) (d) Using the change of variables, set up a double integral for calculating the area of the region D. 1 1 axdy = ]. J. |o(x, y) dudu =/ a(u , v) | du du (e) Evaluate the double integral and compute the area of the region D. Area =
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