Let R be the region bounded by the ellipse x^2/a^2 + y^2/b^2 = 1, where a > 0 and b > 0 are real numbers. Let T be the transformation x = au, y = bv. Evaluate integral integral_R |xy| dA. First, find the Jacobian for the given transformation. J (u, v) = Perform the change of variables and write the new integral in the uv-plane. integral^_ integral^_ () dvdu (Type exact answers.) Now evaluate the integral. integral integral_R |xy| dA =
Show transcribed image textLet R be the region bounded by the ellipse x^2/a^2 + y^2/b^2 = 1, where a > 0 and b > 0 are real numbers. Let T be the transformation x = au, y = bv. Evaluate integral integral_R |xy| dA. First, find the Jacobian for the given transformation. J (u, v) = Perform the change of variables and write the new integral in the uv-plane. integral^_ integral^_ () dvdu (Type exact answers.) Now evaluate the integral. integral integral_R |xy| dA =