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anonymous
 4 years ago
Answer needed! Multiple Choice,
Find the volume obtained by rotating the region bounded by the given curves about y = 1.
anonymous
 4 years ago
Answer needed! Multiple Choice, Find the volume obtained by rotating the region bounded by the given curves about y = 1.

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Rogue
 4 years ago
Best ResponseYou've already chosen the best response.0If you think about it, rotating y = sin x about y = 1 is really the same as rotating y = sin x + 1 about the xaxis.\[V = \pi \int\limits_{a}^{b} (R(x))^2  (r(x))^2 dx\] Our outer radius is just R = sin x + 1. We have no inner radius, so r = 0.\[V = \pi \int\limits_{\pi/2}^{\pi} (\sin x + 1)^2 dx\] I'll leave the integration to you, can you do it?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0Actually, Rogue's evaluation of the problem is not quite right, as you may have figured from the fact that the result of their integral is not a choice. Look at the graphdw:1329417226226:dwso it looks like we do in fact have an inner and outer radius. inner radius=1 outer radius=1+sinx so our integral is\[\pi\int_{a}^{b}r_o^2r_i^2dx=\pi\int_{\pi/2}^{\pi}(\sin x+1)^21^2dx\]now integrate and you will get an answer on the list.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1329417718169:dw
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