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\noindent {\bf Problem statement} Suppose $f(x)=2x^2-x^3$ and
$g(x)=\sin \!\left(\!{{\pi x}\over 2}\!\right)$.

\medskip

\noindent a) Use your calculator to sketch the two functions $y=f(x)$
and $y=g(x)$ on the interval $[0,2]$. Note all the points of
intersection as precisely as you can.

\medskip

\noindent b) What is the exact value of $\int_0^2 f(x)-g(x)\,dx$? Find
a numerical approximation of this value.  What does the value of this
integral tell you about the areas of the regions between the two
graphs?

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