Unformatted text preview: integral. 6. Set up the integral to ﬁnd the arc length of y = xex on the interval [2 , 3]; do not evaluate the integral. 7. Find the arc length of y = e x on the interval [0 , 1]. (This can be done exactly; it is a bit tricky and a bit long.) 9.10 Surface Area Another geometric question that arises naturally is: “What is the surface area of a volume?” For example, what is the surface area of a sphere? More advanced techniques are required to approach this question in general, but we can compute the areas of some volumes generated by revolution. As usual, the question is: how might we approximate the surface area? For a surface obtained by rotating a curve around an axis, we can take a polygonal approximation to the curve, as in the last section, and rotate it around the same axis. This gives a surface...
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 Fall '07
 JonathanRogawski
 Math, Calculus, Arc Length, Derivative, lim

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