\begin{homework}\
\label{homework:12}

\medskip
\exercise
Find the $x$-coordinate of the center of mass of the flat plate bounded
by the $x$- and $y$-axes, the line $x=5$, and the curve
$y=1/\sqrt{1-0.01x^2}$.

\smallskip
\exercise
Find the anti-derivative of 

(a) $\sin(2\pi t)/\sqrt{2+\cos(2\pi t)}$;

(b) $\cos(ax+b)/\sin^8(ax+b)$.

\smallskip
\exercise
Find the volume of the solid obtained by revolving $y=\cos x$ around the
$x$-axis between $x=0$ and $x=\pi/4$.

\smallskip
\exercise
Find the average value of sin${}^nx$ between 0 and $\pi/2$ when $n$ is

(a) 3, (b) 4, (c) 5, (d) 6, (e) 7.

\end{homework}
 
