00:01
Okay, so this is the interval that we'd like to look at, and we're going to start with a u sub.
00:06
So let u equal to the square root of x, and then du, taking the derivative of both sides, is going to be equal to 1 over 2, square root of x, dx.
00:18
And then let's bring this all over to one side.
00:21
So this is going to be equal to 2 times square root of x, but square root of x is u.
00:25
So we can say that this is 2u, d ,u is equal to dx.
00:32
And then let's substitute in.
00:35
So what we've got is that this is equal to the square root of, well, let's take our two out front.
00:42
We're now going to plug that in.
00:44
So two, and then square root of x is equal to you.
00:47
So that's you.
00:49
And then one plus, and then since u is equal to square root of x, then x cubed is u to the sixth.
00:57
And then, well, we had replaced dx with 2u, d...