Question Qi Use spherical coordinates to evaluate the triple integral SII (- – y) dedydz, where D is the solid region defined by the inequalities x2 + y2 + x2 < 9, x > 0 and 2 > 0. [12 marks]

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