How do I determine the volume of a revolved area using integrals?

[Zach:D]

Hello. I am a calculus student currently studying integrals. I am able to logically break down most problems, but I came to a breaking point today. I am trying to understand how to revolve the area between two trigonometric functions about a vertical line. The conditions I am trying to satisfy is when these functions form an area that is apparently symmetric and end on identical y coordinates. To simplify my question, I'll create an example.


Revolve the area enclosed by f(x) and g(x) about the line x= -1 on the interval [0, $$\pi$$]
f(x) = sin(x)
g(x) = -sin(x)


I am having incredible difficulty merely setting up the integral. Clearly, I'll need something like this:



V = $$\pi$$ $$\int$$ ( something + 1)^2 - ( something + 1)^2 dy

I understand the concept of selecting f(y) and g(y) and subtracting the axis' x-coordinate, but I do not understand how to choose which one is an outer radius and which one is an inner radius. Additionally, because the points that they intersect at are identical, I am not sure what bounds to use without getting a bad answer (v=0). I appreciate your time and hope that you will forgive my English.

 

[ialbrekht]

To find area between two functions you have to find integral of module of differences of them.

But in current situation it's a bit easier:
$$sin(x) > -sin(x)$$ on $$[0, \pi]$$
$$v = \int_o^\pi sin(x)-(-sin(x)) dx = 2 \int_0^\pi sin(x) dx$$

My English is also not really good