calculus:resources:calculus_flipped_resources:applications:5.1_area_tex [Department of Mathematics and Statistics, Binghamton University]

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[[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/51graph.png|51graph.png]]\\

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\begin{document}

\begin{frame}
    For each of the two regions described below, sketch the region enclosed by the 
    given curves. Decide whether to integrate with respect to x or y. Draw a typical 
    approximating rectangle and label its height and width. Then find the area.
    \vskip 10pt

    $$y = 2x + 3\qquad    y = 13 - x^2\qquad    x = -1\qquad   x = 2$$
    \vskip 35pt

    $$x = 45 - 5y^2\qquad  x = 5y^2 - 45$$
\end{frame}


\begin{frame}
    Sketch the region enclosed by the given curves. Then find the area.
    \begin{enumerate}[a)]
        \item $$x = 6y^2\qquad  x = 4 + 5y^2$$
        \item $$y = 6 \cos(\pi x)\qquad    y = 12x^2 - 3$$
        \pause
        \item $$y = 4 \cos(6x)\qquad   y = 4 \sin(12x)\qquad  x = 0\qquad  
        x = \pi/12$$
        \item $$y = \sqrt{x}  \qquad y = \frac{1}{2}x\qquad  x = 25$$
        \pause
        \item $$y = |3x|\qquad  y = x^2 - 4$$
    \end{enumerate}
\end{frame}

\begin{frame}
    Two cars, A and B, start side by side and accelerate from rest. The graphs 
    of their velocity functions are given below.
    \begin{figure}[h]\centering{
        \includegraphics[height=1.7in]{51graph.png}}
    \end{figure}
    \begin{enumerate}[a)]
        \item Which car is ahead at time $a$? Explain.
        \item Interpret the area of the shaded region in physical terms.
        \item Which car is ahead after $1.5a$ minutes? Explain.
    \end{enumerate}
\end{frame}

\begin{frame}
    Find the number $b$ such that the line $y = b$ divides the region bounded 
    by the curves $y = 4x^2$ and $y = 16$ into two regions with equal area.
\end{frame}


\end{document} 
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