Find the volume of the “flying saucer” produces by rotating y = sin(x) around the y axis

[KrabLord]

I can visualize the flying saucer. From my understanding, to find the volume, we find the formula for a circle which would fit in the volume for all input values. However, I cannot figure this problem out nor do I understand why the given answer is the answer. So, I would like help with those.

 

[MarkFL]

I would use the shell method here:

[MATH]dV=2\pi x\sin(x)\,dx[/MATH]
Hence:

[MATH]V=2\pi\int_0^{\pi} x\sin(x)\,dx[/MATH]
Are you with me so far?

 

[KrabLord]

Yes, I should have read my notes! Thank you very much!

 

[MarkFL]

Yes, I should have read my notes! Thank you very much!

Are you able to complete the integration to get the indicated result?

 

[KrabLord]

Are you able to complete the integration to get the indicated result?

Yes, I can handle that. Thanks again!