\begin{frame}
  \frametitle{Average Value of a Function}
  
  \begin{block}{}
    The average value $f_{\text{avg}}$of a function $f$ on an interval $[a,b]$ is:
    \begin{talign}
      f_{\text{avg}} = \frac{1}{b-a} \int_a^b f(x) \, dx
    \end{talign}
  \end{block}
  \pause\medskip

  \begin{exampleblock}{}
    Find the average value of the function $f(x) = 1+ x^2$ on the interval $[-1,2]$.
    \pause
    \begin{talign}
      f_{\text{avg}} 
      &= \mpause[1]{ \frac{1}{2-(-1)} \int_{-1}^2 f(x) dx}\\
      \mpause{ &= \frac{1}{3} \left(x + \frac{1}{3}x^3\right)\Big]_{-1}^2} \\
      \mpause{ &= \frac{1}{3} \left(2 + \frac{1}{3}2^3 - \left((-1) + \frac{1}{3}(-1)^3\right)\right) } \\
      \mpause{ &= \frac{1}{3} \left(2 + \frac{8}{3} + 1 + \frac{1}{3}\right) } 
      \mpause{ = 2 } 
    \end{talign}
  \end{exampleblock}
  \vspace{10cm}
\end{frame}