\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Suppose that $f$ is a continuous function (defined for all
$x$) and that the values of the following integrals are known:

\medskip

\centerline{$ \int_0^1 f(x)\,dx=5\thinspace ;\ \;
\int_{-1}^1 f(x)\,dx=3\thinspace ;\ \;
\int_0^2 f(x)\,dx=8\thinspace ;\ \;
\int_0^4 f(x)\,dx=11\thinspace .
$}

\medskip

\noindent Evaluate these integrals: 

\medskip

\noindent a) $\int_0^2 f(2x)\,dx$ \qquad 
b)$\int_0^{\pi} \sin x f(\cos x)\,dx$ \qquad 
c)$\int_2^3
xf(8-x^2)\,dx$.  

\medskip

\noindent {\bf Hint} Use substitutions, such as $u=\cos x$ in b).










\vfil\eject\end