I am given that the vector $\mathbf{u} = 2z^{3}re_{r} + 3z^{2}r^{2}e_{z}$ in the cylindrical polar coordinates.
I am required to find the surface integral but instead of using the Gauss theorem I wanted to do it directly.
$\int_{a}^{b}u. \,dA $
What is $dA$ equal to?