Should I expect the same volume if pi is factored out in the disk method?

[Aria.M]

I'm working through a problem about finding the volume of a solid of revolution using the disk method, and I've set up my integral with the radius in terms of x. But when I evaluate it, my answer has a constant pi term, while the textbook solution has the constant factored out front. Is my approach wrong, or is this just a different way of writing the same final numerical value?

[James.M]

Usually this is the same. If you write V = pi times the integral of R(x) squared, you can pull the pi out front and the final number doesn't change. It's just two ways of writing the same thing.

[BenjaminJR]

I've done that myself: left the pi inside the integral, then evaluated, and compared to the textbook form with pi out front. The numbers matched in the end.

[Oliver.L]

If you see a mismatch, double check that you're squaring R correctly and that you used the same bounds. Sometimes a slip in the algebra makes it look like a different constant is in play, but usually it's just the pi moving.

[NicholasTM]

Are you sure you actually get the same decimal when you compare the two forms, or is there a hidden mismatch in simplification?