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\noindent{\Large{\textsc{Complex Variables\hfill Assignment 7.2  \\ Spring 2020 \hfill Due March 18}}}

\large

\vspace{1cm}

\begin{exercise}
Textbook exercise III.1.1.
\end{exercise}

\begin{exercise}
Let $\Omega \subset \R^2$ be a domain.  Suppose $\gamma : [a,b] \to \Omega$ is a $C^1$ path and that $\omega = P \, dx + Q \, dy$ be a $C^0$ 1-form on $\Omega$.  If $\phi : [\alpha, \beta] \to [a,b]$ is a $C^1$ reparametrization of $[a,b]$, prove that
\[
\int_{\gamma \circ \phi} \omega = \int_{\gamma} \omega.
\]
\end{exercise}

\begin{exercise}
With hypotheses as in the preceding exercise, show that
\[
\int_{-\gamma} \omega = - \int_{\gamma} \omega.
\]
\end{exercise}


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