(1)
先对X积分,再对Y积分,
（D)双积分:(X^2+Y^2-X)dσ
=(D)双积分:(x^2+y^2-x)dxdy
=积分:(0,2)dy积分(y/2,y)(x^2+y^2-x)dx
=积分:(0,2)dy[x^3/3+xy^2-x^2/2]｜(y/2,y)
=积分:(0,2)[(y^3/3+y^3-y^2/2)-(y^3/24+y^3/2-y^2/8)]dy
=积分:(0,2)[19y^3/24-3y^2/8]dy
=[(19/24)(y^4/4)-(3/8)(y^3/3)]｜(0,2)
=(19/24)(16/4)-(3/8)(8/3)
=19/6-1
=13/6.
(2).∫∫{√（1-x^2-y^2）}dσ D是区域x^2+y^2=0.y>=0
做极坐标变换:
x=rcosb,y=rsinb
则:
0