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I was working through some problems in my spare time when I realized that I wasn't so satisfied with my understanding of how to use Greens theorem with holes. Can someone refresh my memory?

More specifically:

Lets say I want to take the line integral in some vector field of a curve C which is the union of the circle of radius 1 and the circle of radius 2 (meaning that the region of integration would be between r=1 and r=2).

How do I go about doing this again? The book says that sometimes I can just take the line integral around the outer curve and ignore the inner curve but doesn't say when/why this can be done.

Thanks.

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# Green's Theorem w/Holes

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