\begin{frame} \frametitle{The Area below a Curve} \begin{alertblock}{} How to compute the area below a curve? \end{alertblock} \medskip \begin{center} \scalebox{.8}{ \begin{tikzpicture}[default] \def\mfun{(4*((\x+\mfunshift)/4)^2)} \diagram[1]{-.5}{4.5}{-.4}{4.5}{1} \diagramannotatez \diagramannotatexx{1/.25,2/.5,3/.75,4/1} \diagramannotateyy{1/.25,2/.5,3/.75,4/1} \def\mfunshift{0} \begin{scope}[ultra thick] \draw[cred] plot[smooth,domain=0:4,samples=20] (\x,{\mfun}); \draw[draw=none,fill=cred,opacity=.5] (.5,0) -- plot[smooth,domain=0:4,samples=20] (\x,{\mfun}) -- (4,0) -- (0,0) -- cycle; \end{scope} \end{tikzpicture} } \end{center} \pause \begin{exampleblock}{} Idea: \begin{itemize} \pause \item divide the area in vertical strips of equal width \pause \item approximate the area using rectangles \end{itemize} \end{exampleblock} \vspace{10cm} \end{frame}