Question

Compute the flux of integral(( x^2i+2y^2j+3z^2k) . dA) where S is the surface of the box enclosing the region 1<=x<=2, 0<=y<=1, 0<=z<=1

Answer 1

\[\int\limits_{s}(x^{2}i+2y^{2}j+3z^{2}k) .dA\]

Answer 2

make use of divergence theorem.

Answer 3

or do you need to do with surface integrals for each side?

Answer 4

I need to do ti with the surface integrals of each side

Answer 5

to calculate flux through the above surface, evaluate the following integral
\[ \int_{0}^{1}\int_{0}^1 (x^2 , 2y^2 , 3z^2).(i, 0, 0) dydz \big|_{x=2}\]

calculate flux through every (altogether 8) surfaces.