Author Topic: Quiz-4-6101 C  (Read 282 times)

Jiaqi Bi

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Quiz-4-6101 C
« on: October 23, 2020, 08:37:43 AM »
Question: $$\int_\gamma sin(z)dz,$$
where $\gamma$ is any curve joining $i$ to $\pi$
Solution:\begin{align*}
&\int_\gamma sin(z)dz\\
&=\int_{i}^{\pi} sin(z)dz\\
&=-cos(z) \Big|_{i}^{\pi}\\
&=-(cos(\pi)-cos(i))\\
&=1+cos(i)
\end{align*}