- #1

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Use the fact that [tex]\int_S \vec{v} \cdot d\vec{S}=\int_S \vec{v} \cdot \frac{\nabla f}{\partial f/\partial x} dy\ dz[/tex]

to evaluate the integral for ##S=\{(x,y,z):y=x^2 ; 0 \geq x \geq 2; 0 \geq z \geq 3 \}## and ##\vec{v}=(3z^2, 6, 6xz)##.

Attempt at a Solution:

I'm having trouble setting up this integral. If I knew what ##f## was, I could easily calculate the gradient, as well as the partial wrt to x. I'd still need to figure out the limits of integration though.