# Integral Over A Region

1. Mar 23, 2009

### azdang

I have to compute the Index around a positively-oriented loop that surrounds the origin. I can use the loop given by (x(s),y(s))=(cos(s),sin(s)), 0<=s<=2*pi.

The first example is:

x' = ax, y' = by, with a>0 and b>0

The formula for the Index around the loop is:
$$\frac{1}{2\pi}\int\frac{PdQ-QdP}{P^2+Q^2}$$ over L, where x'=P and y'=Q

So for this first example, I get:

$$\frac{1}{2\pi}\int\frac{ab(x-y)}{(ax)^2+(by)^2}$$ over L

But I COMPLETELY forget how to take integrals over regions. Can anyone help me out? Thank you.