\begin{frame} \frametitle{The Substitution Rule for Definite Integrals} Methods for evaluating a \emph{definite integral using substitution}:\vspace{-.5ex} \begin{talign} \int_a^b f(x) dx \end{talign}\vspace{-1.5ex} \pause \begin{block}{Method 1} \begin{itemize} \pause \item evaluate the indefinite integral $\int f(x) dx$ using substitution \pause \item then use the Fundamental Theorem $\int_a^b f(x) dx = \int f(x) dx \big]_a^b$ \end{itemize} \end{block} \pause \begin{exampleblock}{} \begin{malign} \int_0^4 \sqrt{2x+1}\,dx = \mpause[1]{\int \sqrt{2x+1} \, dx \big]_0^4} \mpause{ = \frac{1}{3}(2x+1)^{\frac{3}{2}}\big]_0^4 } \mpause{ = 9 - \frac{1}{3} } \mpause{ = \frac{26}{3} } \end{malign} \end{exampleblock} \pause\pause\pause\pause\pause \subruled \end{frame}