# Integral Q with vector field

1. May 18, 2006

### ElDavidas

Again, I'm stuck on a question:

"Let C be the region in space given by $0 \leq x,y,z \leq 1$ and let $\partial C$ be the boundary of C oriented by the outward pointing unit normal. Suppose that v is the vector field given by

$$v = (y^3 -2xy, y^2+3y+2zy, z-z^2)$$.

Evaluate $$\int_{\partial C} v . dA$$

Stating clearly any result used"

Last edited: May 18, 2006
2. May 18, 2006

### Benny

Well if the integral you need to evaluate is a surface integral then just use Gauss/Divergence theorem. But in this context, your notation, more specifically the dA, is unfamiliar to me.

3. May 18, 2006

### ElDavidas

This is what I don't understand. If you have to calculate the area, why are you given x,y, and z? Unless it's the surface of the cube you have to find out. I'm not sure how to go about doing that though

4. May 18, 2006

### Benny

If it's the surface integral over the cube then it should be

$$\int\limits_{}^{} {\int\limits_{\partial W}^{} {\mathop v\limits^ \to } } .d\mathop S\limits^ \to = \int\limits_{}^{} {\int\limits_{}^{} {\int\limits_W^{} {\nabla \bullet \mathop v\limits^ \to } } }$$

Where the terminals of the triple integral go from -1 to 1 for each of x,y and z.

5. May 19, 2006

### ElDavidas

Sorry but I don't understand this notation. Are you integrating the gradient of v?

6. May 19, 2006

### Benny

It's the divergence of v (there is a dot in between grad and v). If you are unsure about what the problem is asking then you should ask whoever set the question. If it is a textbook problem then surely there should be a related theory section with relevant formulas and explanations.