Originally Posted by

**Thomas154321** Evaluate

$\displaystyle I = \int \nabla \cdot \bold F dV$

for $\displaystyle \bold F = \sqrt{x^2+y^2}(x\bold e_1 + y\bold e_2)$ over the volume $\displaystyle x^2 + y^2 \leq R^2, 0 \leq z \leq L$

So I get $\displaystyle I = \oint \bold F \cdot d\bold A$ but can't work out what to replace $\displaystyle d\bold A$ by, for example $\displaystyle (x\bold e_1 + y^2\bold e_2 + \bold e_3) dA$. I think the answer is $\displaystyle (x\bold e_1 + y\bold e_2) dA$ but I don't have a clue how to find that. If it is true which makes it parallel to **F** leading to the answer $\displaystyle R^2A$ which seems reasonable.

Many thanks for any comments. ^_^