# Thread: Volume of a revolved curve

1. ## Volume of a revolved curve

Find the volume generated by revolving the region between $\displaystyle y = sinx$ from $\displaystyle [0,\pi]$ and the line $\displaystyle y = 0$ about the x-axis.

I keep coming up with 0 as an answer, and I know this can't be true. Can someone please tell me what I'm doing wrong?

2. Originally Posted by penguinpwn
Find the volume generated by revolving the region between $\displaystyle y = sinx$ from $\displaystyle [0,\pi]$ and the line $\displaystyle y = 0$ about the x-axis.

I keep coming up with 0 as an answer, and I know this can't be true. Can someone please tell me what I'm doing wrong?
Are you using $\displaystyle V=\int_0^{\pi}\pi(sin x)^2\,dx$?

3. Yes, I realized that I was integrating $\displaystyle sin^2 x$ wrong, and that I had to use the double angle formula. I came up with $\displaystyle \frac{\pi}{2}$

4. Originally Posted by penguinpwn
Yes, I realized that I was integrating $\displaystyle sin^2 x$ wrong, and that I had to use the double angle formula. I came up with $\displaystyle \frac{\pi}{2}$
$\displaystyle \int_0^{\pi}(sin x)^2\,dx=\frac{\pi}{2}$

$\displaystyle V=\int_0^{\pi}\pi(sin x)^2\,dx$

Multiply your answer by $\displaystyle \pi$