Question

calculate the surface ∫ ∫ s 4X dydz-3y dzdx +2zdxdy

Answer 1

$\int\limits^{}_{} {\int\limits^{}_{} {4x} \, dy } \, dz- \int\limits^{}_{} {\int\limits^{}_{} {3y} \, dz } \, dx+ \int\limits^{}_{} {\int\limits^{}_{} {2z} \, dx } \, dy\\\\=4x*[\int\limits^{}_{} {} \, dy]*[\int\limits^{}_{} {} \, dz]-3y*[\int\limits^{}_{} {} \, dz]*[\int\limits^{}_{} {} \, dx]-2z*[\int\limits^{}_{} {} \, dx]*[\int\limits^{}_{} {} \, dy]\\\\=4xyz-3yzx+2zxy\\\\=3*xyz$

In the above integration, we can separate the integrations, wrt x, y and z , independent of one another .  Reason is that  integrand expression does not depend on the variable wrt which we integrate..  It can be treated as a constant.