\begin{homework}\
\label{homework:15}

\medskip
\exercise
Use inverse trig substitution to find $\int dx/\sqrt{r^2-x^2}$, where
$r$ is a constant (we evaluated this earlier using a $u$-substitution).

\smallskip
\exercise
Find the anti-derivative of 

(a) $1/\sqrt{x^2+r^2}$, 

(b) $1/\sqrt{ x^2-r^2}$.

\smallskip
\exercise
Find the center of mass of the uniform flat plate bounded by the curve
$y=x\,\arcsin\,x$, the curve $y=-x\,\arcsin\,x$, and the line $x=0.5$.

\smallskip
\exercise
Find the $x$-coordinate of the center of mass of the uniform flat plate
bounded by the $x$- and $y$-axes, the line $x=2$, and the curve
$y=1/\sqrt{x^2+6x+13}$.

\smallskip
\exercise
Find $\int_0^\infty dx/\left((x+2)\sqrt{x^2+4x+5}\right)$.

\end{homework}
 
 
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