Question

Change the order of integration and hence evaluate ∫∫xydydx for x, y ∈[(0, 4a) (x²/√4a, 2ax)]

Answer 1

We have

From y = x²/4a, we get y = 0 and y = 4a

Thus the points of intersection of the parabola y = x²/4a and y = 2√ax are (0, 0) and (4a, 4a) on changing the order of integration we have y varying from 0 to 4a and x varying from y²/4a to 2√ay.

Thus