\begin{frame}
  \frametitle{Antiderivatives / Integrals}

  \begin{exampleblock}{}
    Find all functions $g$ such that
    \begin{talign}
      g'(x) = 4\sin x + \frac{2x^5 - \sqrt{x}}{x}
    \end{talign}
    \pause
    We first simplify
    \begin{talign}
      g'(x) = 4\sin x + 2x^4 - x^{-\frac{1}{2}}
    \end{talign}
    \pause
    Then the general antiderivative of $g'$ is:
    \begin{talign}
      g(x) = \mpause[1]{4(-\cos x)}\mpause{+ \frac{2}{5}x^5} \mpause{ - 2\sqrt{x}} \mpause{+ C}
    \end{talign}
  \end{exampleblock}
  \pause\pause\pause\pause\pause\bigskip
  
  In applications of calculus, finding antiderivatives is common:
  \begin{itemize}
  \pause
    \item we measure the speed, and want the distance traveled
  \pause
    \item we measure the acceleration, and wand to know the speed
  \pause
    \item \ldots
  \end{itemize}
\end{frame}