As long as you can get a general equation for the radius out from the function you revolve around to the function you are revolving, it should work. Fundamentally, I don't think there's much of a difference between rotating around y=3 and rotating around y=x. I wonder why they never do that in calc classes.

>>85
We did that in my calc class. You're right, there's no real difference. In that case you could just shift it all to y=0 if you felt like it, the vol/SA will be the same. But rotating about y=(some constant) is much different than rotating about something nonlinear.

We covered a very similar problem involving rotating y=sqrt(x) about the line y=x on the interval (0,1)

How we tackled it was we approached it all from the mindset of vectors. We took the projection of y=sqrt(x) on y=x and then subtracted it from the original vector to get a new vector whose length was the perpendicular distance from y=x to y=sqrt(x). The 'vector' was an ordered pair entirely dependent on x as a variable, so when we found the length of the vector we simply created a function. Then we had to stretch the function out 'cause it was too short (I really don't know how to explain that bit but it makes sense)

At any rate, if you understood a lick of what I said, I think it's a pretty nifty way to get the job done.

If you're rotating about a function which isn't a line, then you need to specify the "orientation" of your discs. For example, if you try to rotate a single point around x^2 at the point (1,1,0) you could have the circle you trace be parallel to the YZ plane or the XZ plane.

>>121
How is orientation specified? It seems that rotating about a line is a special case of rotating about a curve, so you might say that 'orientation is implied' in the R2 euclidean linear case, but how is it explicitly defined and how does it get defined in non-linear R2 cases?