00:01
So here we're going to find the area, the surface area of a curve that's been rotated around the x -axis.
00:09
And so here are parameters.
00:11
And so what we're going to use is our formula for the area, which will be 2 pi and then yds, where y, if we look at what the graph will look like.
00:29
So we have, let's say this is about, it'll be a lot steeper than this, but just for definitely.
00:35
Demonstration purposes.
00:37
So when we rotate this around the y -axis, what it's gonna look like, something like this, something like that, and it'll be this cone shape.
00:55
And so what we're gonna do is break it down into these small segments where it's sort of like a cylinder, but the top is slightly bigger, or slightly smaller than the bottom.
01:09
And so these are called frustrums.
01:11
And so our formula for the area of a frustrum, our formula for the area of a frustrum, our formula for the area of the rotated curve comes from integrating our area of a frustrant formula.
01:24
And so we can sub in what we know for y and ds here.
01:28
So we're going to get 2 pi, this integral is course going from 0 to 1...