Evaluate the double integral _R(x^2+y^2 )dA where R is the region inside the ellipse (x^2/4 + y^2/9 = 1 by completing the steps below. If we use the change of variables x = 2u and y = 3v. What is the new region we integrate over in the uv-plane? Compute the Jacobian of this transformation. Rewrite the integral in terms of u and v and evaluate it in the new coordinate system. Do you think the integral in terms of u, v is easier to calculate than the integral in terms of x, y? Explain your answer. Calculate both integrals. Explain why they are the same value. Why is the second one easier to calculate than the first one