# [SOLVED] Finding volume with integration

• February 24th 2010, 05:56 PM
yzobel
[SOLVED] Finding volume with integration
f(x)=4sinx on (0, pi)
Find the volume of a 3d-solid obtained by rotating this region about the dashed line y=-1

I realize this is just like a regular integration volume equation but I'm having trouble distinguishing the radii.

V= pi (0---pi) (R^2-r^2) dx

Is r=4 and then R=(f(x)-f(-1))? And how would I write this in the above formula so as to be able to integrate it?

• February 24th 2010, 06:34 PM
Quote:

Originally Posted by yzobel
f(x)=4sinx on (0, pi)
Find the volume of a 3d-solid obtained by rotating this region about the dashed line y=-1

I realize this is just like a regular integration volume equation but I'm having trouble distinguishing the radii.

V= pi (0---pi) (R^2-r^2) dx

Is r=4 and then R=(f(x)-f(-1))? And how would I write this in the above formula so as to be able to integrate it?

$V=\pi\int_{0}^{\pi}R^2dx$
$=\pi\int_{0}^{\pi}\left(4Sinx+1\right)^2dx$