\begin{frame}
  \frametitle{The Area below a Curve}

  \begin{exampleblock}{}
    Estimate the area below the curve $f(x) = x^2$ from $0$ to $1$.
  \end{exampleblock}
    
  \medskip
  \begin{minipage}{.49\textwidth}
  \begin{center}
  \scalebox{.65}{
  \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});

      \def\mwidth{4}
      \setcounter{slide}{1}
      \foreach \nrsteps/\mcolor in {3/cred,7/cred,19/cred} {
        \setcounter{roundcounter}{\arabic{slide}}
        \def\mstep{\mwidth/(\nrsteps+1)}
        \def\mfunshift{0}
        \foreach \xx in {0,...,\nrsteps} {
          \def\x{\xx*\mstep}
          \setcounter{tmpcount}{\arabic{roundcounter}}
          \addtocounter{tmpcount}{\nrsteps}
          \onslide<\arabic{slide}>{ 
            \draw[thick,draw=\mcolor!60!black,fill=\mcolor,opacity=.5] ({\x},0) rectangle ({\x+\mstep},{\mfun}); 
            \node[include=\mcolor] at ({\x+\mfunshift},{\mfun}) {};
          }
        }
        \addtocounter{slide}{1}
      }
    \end{scope}
  \end{tikzpicture}
  }
  \end{center}
  \end{minipage}~
  \begin{minipage}{.49\textwidth}
  \begin{center}
  \scalebox{.65}{
  \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});

      \def\mwidth{4}
      \setcounter{slide}{1}
      \foreach \nrsteps/\mcolor in {3/cred,7/cred,19/cred} {
        \setcounter{roundcounter}{\arabic{slide}}
        \def\mstep{\mwidth/(\nrsteps+1)}
        \def\mfunshift{\mstep}
        \foreach \xx in {0,...,\nrsteps} {
          \def\x{\xx*\mstep}
          \setcounter{tmpcount}{\arabic{roundcounter}}
          \addtocounter{tmpcount}{\nrsteps}
          \onslide<\arabic{slide}>{ 
            \draw[thick,draw=\mcolor!60!black,fill=\mcolor,opacity=.5] ({\x},0) rectangle ({\x+\mstep},{\mfun}); 
            \node[include=\mcolor] at ({\x+\mfunshift},{\mfun}) {};
          }
        }
        \addtocounter{slide}{1}
      }
    \end{scope}
  \end{tikzpicture}
  }
  \end{center}
  \end{minipage}
  \begin{talign}
    0.21875 = L_4 \hspace{.5cm}<\hspace{.5cm} &A \hspace{.5cm}<\hspace{.5cm} R_4 = 0.46875
    \\
    \mpause[1]{
      0.2734375 = L_8 \hspace{.5cm}<\hspace{.5cm} &A \hspace{.5cm}<\hspace{.5cm} R_8 = 0.3984375
    }\\
    \mpause{
      0.3087500 = L_{20} \hspace{.5cm}<\hspace{.5cm} &A \hspace{.5cm}<\hspace{.5cm} R_{20} = 0.3587500
    }
    %     \mpause{
    %       0.3234000 = L_{50} \hspace{.5cm}<\hspace{.5cm} &A \hspace{.5cm}<\hspace{.5cm} R_{50} = 0.3434000
    %     }
    %     \mpause{
    %       0.3283500 = L_{100} \hspace{.5cm}<\hspace{.5cm} &A \hspace{.5cm}<\hspace{.5cm} R_{100} = 0.3383500
    %     }
  \end{talign}\vspace{-3ex}

  \begin{exampleblock}{}
  We have obtained an estimation of $A$:
  \begin{itemize}
    \item we can improve the estimation by taking more strips
  \end{itemize}
  \end{exampleblock}
  \vspace{10cm}
\end{frame}