设D={（x,y）／x^2+y^2≤x},求∫∫x^1/2dxdy
问题描述：
设D={（x,y）／x^2+y^2≤x},求∫∫x^1/2dxdy
答
D={(x,y)|x^2+y^2≤x}={(x,y)|(x-1/2)^2+y^2≤1/2}∫∫x^1/2dxdy=∫[0,1]x^1/2dx∫ [-(x-x^2)^1/2,(x-x^2)^1/2]dy=∫[0,1]x^1/2*2(x-x^2)^1/2dx=∫[0,1]2x*2(1-x)^1/2dx令t=(1-x)^1/2,x=1-t^2,dx=-2tdt原式=∫[0,1]2...