Set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the x axis.

Now, to find the derivative is easy.

Not sure why the solution manual shows a - instead of a plus!

Anyways, at this point we have the form

which i can follow along with..

What is going on here? because if i squared everything i would get

no ... you're forgetting the middle term
However, the next step i dont see how the solutions manual got it..?

and why are they attaching y prime on the end? you dont need to explain the 2 pi