Originally Posted by

**InfernoZeus** I'm stuck on a question about complex line integration; I've managed to do some simpler questions, but integrating $\displaystyle \int \exp(it) dt$ is giving me problems. Here's the full question:

Calculate $\displaystyle \int_\gamma |z| dz$ when $\displaystyle \gamma = \{ z : z = \exp(it), -\pi \leq t \leq 0 \}$

So my first step is

$\displaystyle \int_{-\pi}^0 |\exp(it)| * \gamma ' (t) dt$

With $\displaystyle \gamma ' (t) = i \exp(it)$ and $\displaystyle |\exp(it)| = 1$

that becomes

$\displaystyle i \int_{-\pi}^0 \exp(it) dt$

I put that into Wolframm's online integrator and it said that's

$\displaystyle \sin(t) - i \cos(t)$

but I don't get how it works that out, or if it's even correct. TIA