00:01
Here, we're given two equations.
00:02
One is y is equal to the square root of x minus one, and the other one is y is equal to x minus one squared.
00:10
These are both just shifted graphs, so we can graph them fairly easily.
00:13
Square root shifted by one here, and then x squared shifted by one here.
00:19
So we're talking about this region here.
00:21
We want to find the volume of that region when it's rotated about the x -axis.
00:26
So i'm going to rotate down this way.
00:30
Essentially i'm going to have a washer.
00:32
So i'm going to use the integral of pi times the big radius squared minus the little radius squared and integrate that with respect to x over all possible x.
00:43
This is going to give me pi times the integral from where i start, well, they both go through 1 to where they end.
00:49
And if x is 2, these are both 1...