\begin{frame} \frametitle{Antiderivatives / Integrals} \begin{block}{} If $F$ is an antiderivative of $f$ on an interval $I$, \\ then the \emph{most general antiderivative} of $f$ on $I$ is \begin{talign} F(x) + C \end{talign} where $C$ is an arbitrary constant. \end{block} \pause \begin{exampleblock}{} Find the general antiderivatives of the following functions: \begin{itemize} \pause \item $f(x) = \sin x$\\ \pause\medskip $F(x) = \pause -\cos x + C$ \pause\medskip \item $g(x) = x^n$ \quad for $n \ne -1$\\ \pause\medskip $G(x) = \pause \frac{1}{n+1}x^{n+1} + C$ \pause\medskip If $n \ge 0$, then this is valid for any interval. \\\pause If $n < 0$ \& $n \ne -1$, then valid for intervals not containing $0$. \end{itemize} \end{exampleblock} \end{frame}