00:01
So in this question, we're looking for the volume of a solid by rotating the region bounded by a couple of lines.
00:07
So we have y equals 2 minus x, which looks like this, which crosses the y -axis at 2 and the x -axis at 2.
00:22
We also have the curve y equals 4 minus x squared.
00:27
So actually i'm going to need to extend this a little bit.
00:39
So y equals 4 minus x squared, or when x is 2, x squared is 4.
00:44
So we can draw this coming down through here, and we're going to rotate this around the x -axis.
00:57
So we need to extend it for x less than 0, and it's going to look something like this.
01:03
So here's our region, and we're going to rotate it around the x -axis.
01:07
So where are these points of intersection? so we've got this one at x equals 2.
01:13
But what about this one over here? well, we've got 4 minus x squared equals 2 minus x, which gives us x squared minus x minus 2 equals 0, which is x minus 2 x plus 1 equals 0.
01:32
So this is at x equals minus 1...