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Integral Over A Region

  1. Mar 23, 2009 #1
    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:
    [tex]\frac{1}{2\pi}\int\frac{PdQ-QdP}{P^2+Q^2}[/tex] over L, where x'=P and y'=Q

    So for this first example, I get:

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

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