# Thread: Contour Integral where f(z) is not continuous

1. ## Contour Integral where f(z) is not continuous

$\int_C \frac{z+i}{z^3 + 2z^2} dz$ , where C is the circle |z|=1 traversed once counterclockwise.

ok so the parameterisation of the contour gives $e^{\pi i t}, 0 \leq t \leq 2$

but i'm not sure how to continue becuase the $f(z)= \frac{z+i}{z^3+2z^2}$ is undefined at z=0 and at z=-2

2. ## Re: Contour Integral where f(z) is not continuous

Originally Posted by linalg123
$\int_C \frac{z+i}{z^3 + 2z^2} dz$ , where C is the circle |z|=1 traversed once counterclockwise.

ok so the parameterisation of the contour gives $e^{\pi i t}, 0 \leq t \leq 2$

but i'm not sure how to continue becuase the $f(z)= \frac{z+i}{z^3+2z^2}$ is undefined at z=0 and at z=-2
You probably need to use the residue theorem.