2pi radians is a full turn round the axis and the length of the curve is what you are multiplying it by. It maps out the surface area. (I think).
How is the formula derived?
My teacher gave me this explaination, but I didn't get a chance to ask him questions.
Taking the derivative of y
further integration (not typing out the steps)
Where do you get from? Why do you need to find the length of the curve?
You might be right. It's been a while since I did stuff like that.
EDIT: Just read it's the circumference (2 pi r) times the diameter (2r), which would make sense, because if you rotated a circle 180 degrees about the center, the point at either side would travel the length of the circumference.
It is pretty good that you guys still remember. In fact I'm shocked on how much you guys know and remember. I did optimization and Rolle's Theorem a few months ago and now I forgot a lot of it. I have to review them now.
Are you supposed to "understand" calculus? I know how to do calculus, but I don't "understand" it. For example, I don't see how a trigonometric function can substitute for x in certain types of square root integration.