Answer Happy

Find f ² dA where R = {(x, y) | 4x² + 16y² ≤ 64} -a) Pick constants and cy for x = Cru and y = cv so that the ellipse R is transformed to the unit circle in terms of u and v (call the unit circle S = {(u, v) | u²+ v² = 1}). - b) Re-write your integral in terms of u and u, do not worry about the limits of integration. Give your answer as: JI. du dv c) Since we're integrating over a circular region, this integral will most likely be easiest to do using polar (cylindrical) coordinates. Perform a second change of variables and re-write your integral in terms of r and 0. - d) Evaluate this polar (cylindrical) integral to answer your original question.