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Question

Evaluate the integral 4a0yy24a(x2y2x2+y2)dxdy by changing into polar coordinates.

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Solution

For protons co-ordinates
x=at2
y=2at
202t=y/2aa2+44a2t2a2t4+4a2t22adt.
202y/2at24t2+44a2tdndx
Whichgivesanswer=8a23

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