00:01
Here we have the equation y equals x minus x squared.
00:04
And if you graph that, it looks like this.
00:10
Now, if we want to rotate that region bounded by y equals zero, so that's this part, about the y -axis, that means we're going to take some shell here, and we're going to rotate it around like this.
00:22
Create a cylinder, where the surface area of that cylinder is going to be 2 pi times the radius.
00:28
That's the bottom times however high that cylinder is.
00:31
Now that's going to be for some given x.
00:33
Let's integrate over all possible x values and we'll have our answer.
00:38
So for r, well, what's the radius? that's the distance from some x value here to the axis of rotation.
00:45
Well, that's just x...