Volume of surface of revolution formed by rotating....

[ellen930]

Hello!

Find the volume of the surface of revolution formed by rotating the region bounded by y = 0, y = cos(x), and x = 2(pi) about the x-axis.

I'm not really sure how to do this problem! Should I use the shells method? The problem with that though, is it has to be with respect to y and we haven't learned how to do derivatives of inverse trigonometric functions. So I'm not really sure any other way to do it. Any suggestions? Thank you.

 

[skeeter]

Find the volume of the surface of revolution formed by rotating the region bounded by y = 0, y = cos(x), and x = 2(pi) about the x-axis.
you sure it isn't x = 0 instead of y = 0?

\(\displaystyle \L V = \pi \int_0^{2\pi} cos^2(x) dx = \pi^2\)

 

[galactus]

You could use shells, but it'd be trickier than the straightforward disk method skeeter suggested.

\(\displaystyle \L\\8{\pi}\int_{0}^{1}ycos^{-1}(y)dy\)