Here's a similar example for your consideration.
Areas of Surfaces of Revolution
Been beating my head against the wall on an integral for awhile now....
The question is this:
Compute the surface area generated by revolving the curve about the x-axis.
I took the 1st derivative of the equation:
Easy enough. Then I went into my integral:
That didn't look very pretty, and I didn't seem to be getting anywhere trying to solve it (no u-sub, and integration by parts didn't seem to be working), so I tried to manipulate the equation several times to see if a different variation would work...
But I can't find one to work out. My professor stated on the assignment that the integral can be done exactly, otherwise I would have approximated it a long time ago.
Would one of you be able to possibly hint where I'm going wrong, or which form you'd take?
Well now I feel like an idiot. Sure enough, I forgot to place the radical in the denominator when I performed it and didn't give it second thought. 1 / sqrt(x), NOT 1/x. I even looked at it several times. Urgh. Sorry all, and thanks.
That makes the integral nice and easy. What a waste of 3 hours.