
\begin{homework}\
\label{homework:14}

\medskip
\exercise
Find 

\begin{tabular}{lll}
(a) $\disp\int_0^1dx/(4-x^2)$; 
       &(e) $\disp\int_0^1x^4dx/(4-x^2)$; 
           &(h) $\disp\int_0^\infty dx/(x^2+10x+25)$;\\

(b) $\disp\int_0^1x^2dx/(4-x^2)$; 
       &(f) $\disp\int_0^1x^4 dx/(4+x^2)$; 
           &(i) $\disp\int_0^\infty dx/(x^2+10x+29)$;\\

(c) $\disp\int_0^1x^3dx/(4+x^2)$; 
       &(g) $\disp\int_0^\infty dx/(x^2+10x+21)$; 
           &(j) $\disp\int_0^1 dx/(2x^2-x-3)$.\\

(d) $\disp\int_1^\infty dx/(x^2+3x)$;

\end{tabular}

\smallskip
\exercise
Find the center of mass of a uniform flat plate bounded by: 

(a) the lines $x=0$ and $x=2$ and the curves 

\qquad $y=1/(x^2+3x+2)$ and
$y=-1/(x^2+3x+2)$; 

(b) the line $x=1$, the curve $y=x^2$Arctan$\,x$, and the curve
$y=-x^2\arctan\,x$.

\smallskip
\exercise
Find the anti-derivative of sec$\,x=(\cos x)^{-1}$ by the method used
before for odd powers of $\cos x$.  That is, write $(\cos x)^{-1}=(\cos
x)^{-2}\cos x=\cos x/(1-\sin^2x)$.  After making the appropriate
$u$-substitution, you will have a rational function to integrate.

\end{homework}
 
