计算二重积分∫∫（x²+y²）dx,其中D是由y轴及圆周x²+y²=1所围成的在第一象限内的区域

先积x, ∫∫ (x2+y2-y)dxdy =∫[0--->2]dy∫[y/2--->y] (x2+y2-y)dx =∫[0--->2] (1/3x3+xy2-xy) |[y/2--->y]dy =∫[0--->2] (1/3y3+y3-y2-(1/3)(y/2)3-y3/2+y2/2) dy =∫[0--->2] [(19/24)y3-(1/2)y2] dy =[(19/96)y?-(1/6)y3] |[0--->2] =11/6本回答被网友采纳