00:01
We have this triangle that is being, so we have y equals 2x.
00:07
And what we're doing is we're going to take this squeeze between y equals 0 and x equals 1.
00:17
And we are asked to revolve it about the line x equals 2.
00:23
So x equals 2.
00:26
And i don't know how you've learned this, but maybe the best method is to think about the washer method.
00:33
I'm going to do my best to draw out what the washer will look like because as you revolve that piece around, you're getting the entire volume.
00:42
So this giant circle.
00:44
May i let me erase that, though.
00:49
So a giant circle in there.
00:50
And then you need to remove this in the middle.
00:54
So as you go to revolve around, you just have a bunch of washers.
00:59
So what i like to do is think about how it's basically the area of the outer function.
01:04
Pi r squared minus the area of the inner function.
01:09
So those are two different radii, though.
01:12
So i don't really like writing it that way, but i'll write it pi, the integral from zero to, well, you actually want the y value.
01:21
And so if x equals 1, then y is going to equal 2.
01:27
So from 0 to 2.
01:29
And the upper function, or the function that's further away, i actually need to solve this for y.
01:36
So x equals 1 half y...
