00:01
In this question, we're asked to compute the volume obtained by rotating the region enclosed by these three functions about the y -axis.
00:08
So let's draw our region first.
00:11
We have 3x minus 2, which will look like this, and then we have 6 minus x.
00:19
So that will look something like this.
00:22
And then we have x -equal 0, which is right here, the y -axis.
00:27
So the region that we are revolving is this triangle shape right here.
00:34
So we know when we compute our volume using the shell method, it's v equals 2 pi, and we have a to b, and it's x times f of x, x, x, x.
00:49
So our a is going to be zero.
00:52
Our b is going to be right here.
00:56
So that's going to be our b.
00:57
And to calculate b, we can equate our two equations, and then we'll be able to find b.
01:05
So we'll get 3x minus 2 is equal to 6 minus x...