# Answer to Question #16165 in Integral Calculus for diey

Question #16165

∫∫∫2y2z dxdzdy ?

∫∫∫dzdxdy ?

∫∫∫dzdxdy ?

Expert's answer

∫∫∫2y2z dxdzdy =∫∫(∫2y2z dx)dzdy=∫∫ (4yz*x+c1) dzdy=∫ (∫ (4yx*z+c1) dz) dy=∫

(2yx*z^2+c1*z+c2)dy=∫

([2xz^2]*y+[c1*z+c2])dy=xz^2*y^2+[c1*z+c2]*y+c3=xz^2y^2+c1*z*y+c2*y+c3

∫∫∫dzdxdy=∫∫(∫dz)dxdy=∫∫(z+c)dxdy=∫((z+c)x+c2)dy=((z+c)x+c2)*y+c3

(2yx*z^2+c1*z+c2)dy=∫

([2xz^2]*y+[c1*z+c2])dy=xz^2*y^2+[c1*z+c2]*y+c3=xz^2y^2+c1*z*y+c2*y+c3

∫∫∫dzdxdy=∫∫(∫dz)dxdy=∫∫(z+c)dxdy=∫((z+c)x+c2)dy=((z+c)x+c2)*y+c3

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