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Unformatted text preview: 1 /x . (a) Compute the volume of the trumpet formed by rotating the region R about the x-axis. (b) Prove that the surface area of the trumpet is innite. Remember that to prove this you dont need to nd the antiderivative of the resulting integrand, but you can compare this integrand with one with easier antiderivative, and divergent integral. (c) Discuss the apparent counterintuitive results obtained: According to (a), you can ll the trumpet with a nite amount of paint, but according to (b), apparently you need an innite amount of paint to coat the inside of the trumpet. Note: there is an interesting article about this on Wikipedia....
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- Spring '11