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The given integration isI=∭_(D)(x-y)dxdydz.with solid regionx^(2)+y^(2)+z^(2) <= 9The spherical coordinates" but "{:[x=r sin theta cos phi,dv=r^(2)sin theta d gamma d theta d phi],[y=r sin theta sin phi,],[z=r cos theta,gamma:0rarr3],[,theta:0rarr pi//z],[,phi:-pi//2rarr pi//2]:}{:[:.∭_(D)(x-y)dxdydz=int_((phi=-3theta=0)^(pi//2)int_(gamma=0)^(pi//2)int_(gamma=0)^(3){(r sin theta cos phi)-(r sin theta sin phi)}gamma^(2)sin theta drd theta d phi],[=int_(-pi//2)^(pi//2)int_(0)^(pi//2)int_(0)^(3)gamma^(3)sin^(2)theta(cos phi-sin phi)d gamma d theta d phi],[=int_(-pi//2)^(pi//2)int_(0)^(pi//2)[(gamma^(4))/(4)]_(0)^(3)sin^(2)theta(cos phi-sin phi)d theta d phi],[{:=(81)/(4)int_(-pi//2)^(pi//2)[(theta)/ ... See the full answer