∫0a∫0a2−y2(x2+y2)dxdy∫y=0y=a∫x=0x=a2−y2(x2+y2)dxdy
From the above case, limits of integration are
x=0 to x=a2−y2y=0 to y=ax=a2−y2⟹y=a2−x2
So new limits of integration are
∫x=0x=a∫y=0y=a2−x2(x2+y2)dydx∫0a∫0a2−x2(x2+y2)dydx=∫0a2−x2x2dy+∫0a2−x2y2dy=∫0a(x2a2−x2+3(a2−x2)23)dx=∫0ax2a2−x2dx+∫0a3(a2−x2)23dx=16πa4+16πa4
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