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\centerline{\bf Math.~125 Quizz \#11}
\centerline{December 8, 1998}
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Consider the curve $y=x^3$, $0\leq x \leq 1$.
\itemitem{1.} Set up the integral which evaluates the arclength
of this curve.
\itemitem{2.} Set up the integral which evaluates the surface area of
the surface of revolution obtained by revolving this curve about the $x$-axis.
\itemitem{3.} Set up the integral which evaluates the surface area of
the surface of revolution obtained by revolving this curve about the $y$-axis.
\itemitem{4.} Which of the two surface areas is smaller?
{\bf Hint:} You do not need to evaluate these integrals to answer this
question, but you do need to remember a theorem comparing values of
integrals.

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