Question

Answer needed! Multiple Choice,

Find the volume obtained by rotating the region bounded by the given curves about y = -1.

Answer 1

Any ideas?

Answer 2

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?

Answer 3

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 graphso 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.