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\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:

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\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 .
$}

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\noindent Evaluate these integrals: 

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

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










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