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- 9. Let R be a square with vertices (0,0), (1,1), (2,0) and (1, -1) in the xy-plane. It might be useful/helpful to sketch the region R and the region S a) Find the image Sin the uv-plane under the transformation T: x=u + v, y = u - V hint: solve for u by solving for x + y (use system) b)Write the Jacobian Matrix of partial derivatives c) evaluate the determinant of the Jacobian d) Rewrite the integral using a change of variables to u and v with the Jacobian and evaluate the new integral. SSR xydAarrow_forwardIntegrate (x + y) dA, where R = {(x, y):0 < x < 2, x < y < x + 4}. Use the transformation x = 2u and y = 4v + 2u. Hint: Sketch the given region R and then the new region in the uv plane.arrow_forwardPlz answer correctly asaparrow_forward
- Evaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Jo F. dr =arrow_forwardLet B be the region in the first quadrant of the ry-plane bounded by the lines r+y = 1, r + y = 2, (x – y)? I = 0 and y = 0. Evaluate -drdy by applying the transformation u = r+ y, v = x – y 1+x + y Barrow_forwardEvaluate exp{}dA where R is the region in the ry-plane bounded by the trapezoid with vertices (0, 1), (0, 2), (2,0), and (1,0) by a suitable change of variables.arrow_forward
- Let D be the triangular region in the uv-plane with vertices (0, 1), (4, 1), (1, 3) and letG(u, v) = (u − v, 2v).Sketch D in the uv-plane and G(D) in the xy-plane.Find the area of G(D) by using Jac(G)arrow_forwardConsider the transformation x =r cos 0, y=r sin 0, z = z from cylinderical to rectangular coordinates, a(x, y, z) a(r, 0, z) * where r > 0. Find 1 -rarrow_forwardUse the transformation u = x2 –- y²,v = x² + y² to find ff, xydA where R is the region in the first quadrant that is enclosed by the hyperbolas x2 y² = 1, x² – y² = 4 and the circles x² + y? = 4 and x? + y? = 9.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage