Find SS² dA where R = {(x, y) | 4x² + 16y² ≤ 64} R Cyv so that the ellipse R is transformed to the unit circle in terms

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Find Ss Da Where R X Y 4x 16y 64 R Cyv So That The Ellipse R Is Transformed To The Unit Circle In Terms 1 (95.73 KiB) Viewed 10 times

Find SS² dA where R = {(x, y) | 4x² + 16y² ≤ 64} R Cyv 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 : = - a) Pick constants c and cy for x = cxu and y = 1}). - b) Re-write your integral in terms of u and v, do not worry about the limits of integration. Give your answer as: SS 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.