Complex Integrals - Poles of Integration Outside the Curve

[SirFibonacci]

Homework Statement

$\int_{|z-2i|=2}$ = $\frac{dz}{z^2-9}$



2. The attempt at a solution

I know that the contour described by |z-2i|=2 is a circle with a center of (0,2) (on the complex plane) with a radius of 2. The singularities of the integral fall outside of the contour (z+3 and z-3). In this case, is the solution just going to be zero or undefined?

 

[sunjin09]

Your integrand is analytic in a region that contains your contour, what do you know about a closed contour integral of an analytic function?

 

[SirFibonacci]

The integral is 0. Makes sense. Thanks.