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{\bf Math 165: Honors Calculus I}
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{\bf Quiz 5}\quad {\sl Oct.\ 6, 1994}

\begin{enumerate}
\problemspace
\item Use the {\sc Invariance Under Translation} property of
integrals to calculate $\int_{-1}^1 (x+1)^{100}\,dx$.

\answerspace

\problemspace
\item Let $f$ be an integrable function on $[-b,b]$.
  \begin{enumerate}[a)]
  \item Suppose $f(-x) = - f(x)$ for all $x$ in $[-b,b]$.\newline
  Prove that $\int_{-b}^b f(x)\, dx = 0$.
  \answerspace

  \item Suppose $f(-x) = f(x)$ for all $x$ in $[-b,b]$.\newline
  Prove that $\int_{-b}^b f(x)\, dx = 2\int_0^b f(x)\, dx$.
  \answerspace

  \item Find $\int_{-3}^3 x\sqrt{9-x^2}\,dx$.
  \answerspace
  \end{enumerate}

\problemspace
\item Find the area between the graphs of $f(x) = x^2 - 1$ and $g(x) = x$ on
$[-1,1]$.

\end{enumerate}

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