5. (4 points) Let D be the region in the first quadrant bounded by x = y², x = y² – 4, x = 9-y², and x = 16-y². Consider

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5 4 Points Let D Be The Region In The First Quadrant Bounded By X Y X Y 4 X 9 Y And X 16 Y Consider 1 (190.37 KiB) Viewed 13 times

5. (4 points) Let D be the region in the first quadrant bounded by x = y², x = y² – 4, x = 9-y², and x = 16-y². Consider the integral J 2y dA. (a) Explain why it makes sense to apply change of variables to the integral. (b) Define a map T-¹(x, y) = (u(x, y), v(x, y)) from the ry- to the uv-plane which turns D into a simple region. Sketch T-¹(D). (c) Find the Jacobian of T-1. (d) Evaluate the integral with a change of variables.