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\begin{center}
{\Large TEST 2

Math 202}
\end{center}

\begin{itemize}
\item  Do your work on separate paper.  Show all your work and make your work neat.  You will be graded on this!
\item  You can use a calculator and book, but I must be able to follow your work as if you had no calculator and book.  No notes!
\item  You will be graded on both your answer and the work done to get that answer.
\item  You have one hour to finish the questions on the exam.
\end{itemize}



\begin{enumerate}


\item  (20 points) Compute the following integrals
	\begin{enumerate}
	\item  \[  \int \frac{dx}{2^{x}+2^{-x}} \]
	\item  \[  \int \frac{x+1}{x^4+x^2} \; dx \]
	\item  \[  \int_0^1 x\sqrt{1-x^2} \; dx \]
	\item  \[  \int \frac{\sqrt{1-x^2}}{x} \; dx \]
	\end{enumerate}

\newpage

\item  (10 points) Determine if the following integral converges or diverges (don't compute, just show me why it converges or diverges).
	\[ 
	\int_2^\infty \frac{1+\cos x}{\sqrt{x^4+x+1}} \; dx 
	\]


\item  (10 points) Take one of the regions bounded by the curve $y=\sin x$ and the line $y=-1$ and rotate it around the line $y=-1$.
	Find an integral that represents the surface area of the surface that is formed.
	\\(Do not compute this integral, just get the integral.)


\item  (10 points) 
	\begin{enumerate}
	\item  Find an integral that represents the length of the curve 
		\[ 
		y=\frac{1}{6}(x^3+3x^{-1})
		\]
		 over the interval $1 \leq x \leq 3$.
	\item  Extra Credit (3 points): Compute the integral
	\end{enumerate}
	

\item  (10 points) Determine how many subdivisions (find $n$) you would need to approximate within $10^{-5}$ the following integral
	using Simpson's rule (don't find the approximation, just find $n$).
	\[
	\int_1^3 \frac{dx}{3+2x}
	\]




\end{enumerate}

\end{document}







