\begin{frame} \frametitle{The Substitution Rule: Exercises} \begin{exampleblock}{} Evaluate \begin{talign} \int_0^1 \cos(\pi x/2)\, dx \end{talign} \pause We take $u = \pause \pi x/2$\pause, then $u' = \pause \pi/2$ \pause and \begin{talign} \int_0^1 \cos(\pi x/2)\, dx \mpause[1]{ &= \int_{u(0)}^{u(1)} \cos(u) \, \frac{du}{\pi/2} }\\ \mpause{ &= \frac{2}{\pi}\int_{0}^{\pi/2} \cos(u) \, du }\\ \mpause{ &= \frac{2}{\pi} \left( \sin u\big]_{0}^{\pi/2} \right) }\\ \mpause{ &= \frac{2}{\pi} \left(\sin(\pi/2) - \sin(0) \right)}\\ \mpause{ &= \frac{2}{\pi} } \end{talign}\vspace{-1.5ex} \pause\pause\pause\pause% \end{exampleblock} \end{frame}