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\problemgrouptitle{Area Between Curves}

\begin{problemblock}{Find the area of the region bounded by the given curves.}

\lab{\addtoanswerkey{\begin{multicols}{2}}}

\item $y=x^2-3x+8$ and $y=4x-x^2$ over the closed interval $[-1,2]$\,.
\answer{$\displaystyle\frac{39}{2}$ units$^2$}

\item $y=x^2-5x-1$ and $y=x-6$ over the closed interval $[1,6]$\,.
\answer{$\displaystyle 13$ units$^2$}

\item $y=x^2+6$,\ \  $y=2x^2+2$
\answer{$\displaystyle \frac{32}{3}$ unit$^2$}

\item $x=2y^2$,\ \  $x=y^2+4$
\answer{$\displaystyle \frac{32}{3}$ unit$^2$}

\item $y=x^2-2x$,\ \  $y=x-2$
\answer{$\displaystyle \frac{1}{6}$ unit$^2$}

\item $y=0$,\ \  $y=2x$,\ \  $x+y=3$
\answer{$\displaystyle 3$ unit$^2$}

\item $\displaystyle y=\frac{8}{x^2}$, $y=x$, $y=4x^2+4x$ and lying in the first quadrant ($x>0$ and $y>0$)\,.
\answer{$\displaystyle\frac{16}{3}$ units$^2$}

\end{problemblock}

\lab{\addtoanswerkey{\end{multicols}}}
