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\begin{frame}
  \frametitle{The Substitution Rule for Definite Integrals}

  \subruled
  
  \begin{exampleblock}{}
    \vspace{-.75ex}
    \begin{talign}
      \int_0^4 \sqrt{2x+1}\,dx 
    \end{talign}
    \pause
    We choose $u = \pause 2x+1$. \pause Then $u' = \pause 2$\pause, and hence
    \begin{talign}
      \int_0^4 \sqrt{2x+1}\,dx 
      \mpause[1]{&= \int_{u(0)}^{u(4)} \sqrt{u}\, \frac{du}{2} }
      \mpause{= \frac{1}{2} \int_{1}^{9} \sqrt{u}\, du }\\
      \mpause{&= \frac{1}{2} (\frac{2}{3}u^{\frac{3}{2}}) \Big]_1^9}
      \mpause{=  \frac{1}{2} (\frac{2}{3}9^{\frac{3}{2}} - \frac{2}{3}1^{\frac{3}{2}})}\\
      \mpause{&=  \frac{1}{2} (\frac{2}{3}\sqrt{9}^3 - \frac{2}{3})}
      \mpause{=  \frac{27}{3} - \frac{1}{3}}
      \mpause{=  \frac{26}{3}}
    \end{talign}
  \end{exampleblock}
  \vspace{10cm}
\end{frame}