question 27

27-30. Double integrals-transformation given To evaluate the fol- do lowing integrals, carry out these steps. a. Sketch the original region of integration R in the xy-plane and the new region S in the uv-plane using the given change of variables. b. Find the limits of integration for the new integral with respect to u and v. of c. Compute the Jacobian. n d. Change variables and evaluate the new integral. 27. xy dA, where R is the square with vertices (0, 0), (1, 1), (2, 0), R and ( 1, - 1); use x = u + v, y = u - v. 28. | x 2 y dA, where R = { ( x , y ) : 0 s x 5 2, x = y s x+ 4); R bos use x = 2u, y = 4v + 2u. 29. x2 V x + 2ydA, where R = { (x, y) : 0 S x 2, R -x/2