Question

Evaluate the given integral over the solid ellipsoid

Answer 1

x=au , y=bv,z=cw jacobian=abc (x2/a2)+(y2/b2)+(z2/c2)<=4 u2+v2+w2<=4 ???2|xyz|dxdydz =???2|aubvcw| abc du dv dw =(abc)2???2|uvw| du dv dw in spherical coordinates u=?sin?cos?,v=?sin?sin?,w=?cos? u2+v2+w2=?2 u2+v2+w2<=4=22 ==>0<=?<=2...