∫y=01∫x=y22−y22x2+y2ydxdy
In this x and y are from 0<y<1 and y<x<22−y2
So we can change it as 0<x<1 and x<y<2−4x2
∫y=01∫x=y22−y22x2+y2ydxdy=∫x=01∫y=x2−4x22x2+y2ydydx∫01∫x2−4x22x2+y2ydydx=41(3x2+8−22x)=∫0141(3x2+8−22x)dx=41(211+32ln(47+33)−2)=41(211+32ln(47+33)−2)=0.39554
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