Toronto Math Forum
MAT3342020F => MAT334Tests and Quizzes => Quiz 4 => Topic started by: Jiaqi Bi 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*}