# Gauss's Theorem

1. Nov 24, 2009

### Somefantastik

1. The problem statement, all variables and given/known data

C is triangle (0,0), (4,0), (0,3). R is the enclosed region. Compute the following integral, where n is the outward pointing normal:

$$\int_{C} \left(4x-y^{2}\right)n^{1}ds$$

where $$n^{1} = \widehat{i} \cdot \widehat{n}$$

2. Relevant equations

3. The attempt at a solution

I can't remember how to get the normal vector, can someone start me out there?

2. Nov 24, 2009

### Dick

There are three normal vectors, one for each side of the triangle that encloses the region. If the vector (a,b) is a tangent to a side then (-b,a) is a normal, isn't it? It's not necessarily a unit normal, but you should know how to fix that. Is that enough to get you started?

3. Nov 26, 2009

### Somefantastik

So to evaluate this integral, should I separate it into 3 sub integrals over the 3 sides, using the corresponding normals?

4. Nov 26, 2009

### Somefantastik

Also, is it necessary to parameterize before integrating? I'm getting hung up on the little details and missing then big picture.

5. Nov 27, 2009

### Dick

Yes, separate it into three integrals. Decide which direction around the triangle you are going. Then parameterize each side by length, integrate and add them up.