Integrating over Triangle C: Computing Normal Vector

[Somefantastik]

Homework Statement

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}

Homework Equations

The Attempt at a Solution

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

 

[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?

 

[Somefantastik]

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

 

[Somefantastik]

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

 

[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.