00:01
Here, we're given the equation that x is equal to y times 19 minus y, x equals 0, and we want to rotate this about the y axis.
00:10
So we'll start off by drawing this graph.
00:12
This is a parabola on its side.
00:14
It crosses at zero and at 19.
00:17
And it's a negative, so it looks like this.
00:21
And then we're going to go rotate this region.
00:25
So the first thing we need to figure out is what is this point here? because that's going to basically tell us a lot of information.
00:31
But as i said, that's just 19.
00:34
So what we need to do then is figure out if we're rotating this about the y -axis, that would be this way.
00:40
This looks to me like it's just a simple disk method.
00:45
So we'll take the integral of pi times the radius squared...