18. Consider the mapping defined by the two equations x- u²². y = 20. (a) Compute the Jacobian determinant J(u, v). Proof of the transformation formula in a special case 401 (b) Let T denote the rectangle in the uu-plane with vertices (1, 1), (2, 1), (2, 3), (1, 3). De- scribe, by means of a sketch, the image S in the xy-plane. с (c) Evaluate the double integral 55 xy dx dy by making the change of variables x²-0², y-2ut, where C-((x, y) | x² + y ≤1). 19. Evaluate the double integral W I(p, r)= dx dy (p"+x²+ y²) over the circular disk R = {(x, y) | x²+ y ≤). Determine those values of p for which Ip, r) tends to a limit as r+co. In Exercises 20 through 22, establish the given equations by introducing a suitable change of variables in each case. 20. f(x) dx dy =), where S = {(x, y) +50 21. fax + by + c) dx dy = 2√²f(u√a² + b² + c) du, where S ((x, y) | x + y ≤1) and a²+b² 0. 22. fixy) dx dy = log 2f(u)du. where S is the region in the first quadrant bounded by thecurvesxy 1, xy-2, yx, y -4x. 20 MacBook Pro