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

1. anonymous

2. anonymous

Any ideas?

3. Rogue

If you think about it, rotating y = sin x about y = -1 is really the same as rotating y = sin x + 1 about the x-axis.$V = \pi \int\limits_{a}^{b} (R(x))^2 - (r(x))^2 dx$ 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?

4. TuringTest

Actually, 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 graph|dw:1329417226226:dw|so it looks like we do in fact have an inner and outer radius. inner radius=1 outer radius=1+sinx so our integral is$\pi\int_{a}^{b}r_o^2-r_i^2dx=\pi\int_{-\pi/2}^{\pi}(\sin x+1)^2-1^2dx$now integrate and you will get an answer on the list.

5. TuringTest

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