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\begin{center}
{\Large Warm-Up Problems

January 24, 2003}
\end{center}

\begin{enumerate}

\item  Compute the following integrals, interpret the result geometrically for the definite integrals.
	\begin{enumerate}
	\item  \[ \int 3\sin(x) \; dx\]
	\item  \[ \int_{0}^{1} x^{7/3}\; dx \]
	\item  \[ \int \sec^2 x +1 \; dx \]
	\item  \[ \int_0^{1} \frac{1}{t^2+1} \; dt \]
	\end{enumerate}

\item  Suppose you know the following definite integrals:
	\[
	\int_{1}^{3}f(x)\;dx=4 \qquad \int_2^5 f(x)\;dx=-7 \qquad \int_3^5 f(x)\;dx=1
		\qquad \int_1^5 g(x) \; dx=-2
	\]
	Find the following integrals:
	\begin{enumerate}
	\item  \[ \int_1^5 f(x)\; dx \]
	\item  \[ \int_2^3 f(x)\; dx \]
	\item  \[ \int_1^5 f(x)+g(x) \; dx \]
	\item  \[ \int_1^5 4f(x)-3g(x) \; dx \]
	\end{enumerate}

\item  Find $a$ so that
	\[
	\int_1^a x^2 \; dx = 5
	\]

\end{enumerate}



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