Finding Volume Using the Sine Function and Disc Method

[cathy]

Homework Statement

Find the volume generated by revolving one arch of the curve y = 5 sin(x) about the x-axis.




The attempt at a solution

So I figured this would create a disc so I would have to use that the volume is ∏r^2 where r=sinx, r^2= (sin(x))^2 and that the way I should set this up is as shown:

5∏∫[sin(x)]^2 from 0 to pi. And then I would replace that with the trig identities and so on. However, this is not giving me the correct answer. Is this integral wrong?

 

[Curious3141]

Homework Statement

Find the volume generated by revolving one arch of the curve y = 5 sin(x) about the x-axis.




The attempt at a solution

So I figured this would create a disc so I would have to use that the volume is ∏r^2 where r=sinx, r^2= (sin(x))^2 and that the way I should set this up is as shown:

5∏∫[sin(x)]^2 from 0 to pi. And then I would replace that with the trig identities and so on. However, this is not giving me the correct answer. Is this integral wrong?

r = 5sin x. You forgot to square the 5.

And not to be pedantic, but ∏r^2 is not the volume of anything. The enclosed volume of a cylinder is $\pi r^2h$, where h is the height. Applied here the volume integral is $\pi\int_a^by^2dx$.

 

[cathy]

Oh! Thank you so much. I did this problem a million times, and it was such a simple mistake. :)