将对坐标的曲面积分∫∫∑x2y2zdxdy化为二重积分,其中∑分别为:
(1)球面x2+y2+z2=R2上半部分的上侧;
(2)球面x2+y2+z2=R2下半部分的下侧;
(3)球面x2+y2+z2=R2下半部分的上侧.
(1)∫∫∑x2y2zdxdy=∫∫Dxyx2y2 √(R2-x2-y2)dxdy (2)∫∫∑x2y2zdxdy=∫∫Dxyx2y2 √(R2-x2-y2)dxdy (3)∫∫∑x2y2zdxdy=-∫∫Dxyx2y2 √(R2-x2-y2)dxdy
将对坐标的曲面积分∫∫∑x2y2zdxdy化为二重积分,其中∑分别为:
(1)球面x2+y2+z2=R2上半部分的上侧;
(2)球面x2+y2+z2=R2下半部分的下侧;
(3)球面x2+y2+z2=R2下半部分的上侧.
(1)∫∫∑x2y2zdxdy=∫∫Dxyx2y2 √(R2-x2-y2)dxdy (2)∫∫∑x2y2zdxdy=∫∫Dxyx2y2 √(R2-x2-y2)dxdy (3)∫∫∑x2y2zdxdy=-∫∫Dxyx2y2 √(R2-x2-y2)dxdy