Question

Set up an integral for the volume of the solid obtained by rotating about the line x=1 the region under the curve y=x*(1-x^2)^(1/2), x in [0,1].

Answer 1

I just want to make sure I've set it up correctly before I start evaluating it. I have\[2\pi\int\limits_{0}^{1}(1-x)x\sqrt{1-x^2} dx\]

Answer 2

Yes, your set up is correct.