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\begin{frame}
\frametitle{The Definite Integral}

\begin{exampleblock}{}
Evaluate the Riemann sum for
\begin{talign}
f(x) = 2x-5
\end{talign}
from $0$ to $6$ using $3$ strips and right endpoints as sample points.
\pause\medskip

We have:
\begin{itemize}
\pause
\item the width of the strips is $\Delta x = \pause (6-0) / 3 \pause = 2$
\pause
\item the intervals of the strips are \pause $[0,2]$, $[2,4]$, $[4,6]$
\pause
\item the right endpoints are \pause $x_1 = 2$, $x_2=4$, $x_3 = 6$
\pause
\item the values at $x_i$'s are \pause $f(x_1) = -1$\pause, $f(x_2) = 3$\pause, $f(x_3) = 7$
\end{itemize}
\pause\medskip
Thus the Riemann sum using $3$ strips and right endpoints is:
\begin{talign}
R_3 = \sum_{i=1}^3 f(x_i)\cdot \Delta x = \mpause[1]{2\cdot (-1)} \mpause{+ 2\cdot 3} \mpause{+ 2\cdot 7}
\mpause{= 18}
\end{talign}
\end{exampleblock}
\end{frame}