Problem 3 The integral: / / sin (x ) d A where R denotes the trapezoidal region with vertices (1,0), (2,0), (0,2), and (0, 1) is difficult to Problem 4 integrate directly. Instead: Problem 5 (a) Consider the transform u = y - x and u = y + x suggested by the integrand. Problem 6 Problem 7 (b) Find the inverse transform T' in the form x = F(u, v) = E and y = G(u, U) = (c) Find the image of R. () Find the image of the side S] joining the vertices (1,0) and (2,0): U = z , for E SUS M (ii) Find the image of the side S2 joining the vertices (2,0) and (0,2): U = , for I SUS (ii) Find the image of the side S3 joining the vertices (0,2) and (0,1): U = z , for I SUS E (iv) Find the image of the side S4 joining the vertices (1,0) and (0, 1): U = E , for E SUS (d) Find the Jacobian of the transformation (with alphabetical ordering): E E E E (e) Write the transformed integral: S S dudv, where a = , b = ,C= , and d = E (f) Evaluate the integral: E NOV 4 A