Find surface integral via divergence theorem

38 Views Asked by At

Evaluate the surface integral $\int \int F • n dA$ by the divergence theorem. Show the details

$$F = [x^{2}, 0, z^{2}]$$ S is the surface area of the box $|x| \leq 1$, $|y| \leq 3$, $0 \leq z \leq 2$

So instead of finding the parametric equation of the box which I don't know... Gauss's theoreum of divergence allows us to find the divergence of F and take the triple integral:

$$div F = 2x + 2x$$

so

$$\int_0^2 \int_{-3}^3 \int_{-1}^{-1} 2x + 2z\, dx dy dz$$

Is that setup right? Can someone help me with the triple integral from here?