00:03
Okay, and this problem, what we want to do is express the arc length as an integral for y equals x to the fourth between x equals 2 and x equals 6.
00:11
And if you look back on pages 467 to 468, the formula here shown in red was derived for finding the arc length.
00:20
So what we need to do is express our circumstances in this form.
00:24
So first of all, let's kind of get a visual of what it is we're looking at.
00:26
We have a version of x to the fourth, right, which looks something like this perhaps.
00:32
And what we're looking at is from x equals 2 to 6, we're interested in the arc length of that curve.
00:40
So what we're trying to identify is the length of this curve here, this arc length.
00:47
So what we need to identify in order to fit the formula here is we need to first find our limits of integration.
00:54
And that's fairly easy.
00:55
They gave those to us here as 2 and 6.
00:58
So we're interested in the arc length from 2 to 6.
01:03
And what we other piece of this puzzle that we need is the derivative of the function that we're looking at.
01:09
So what we want to do is we want to take our function, which is f of x equals x to the fourth, and find the derivative of that function.
01:17
The derivative of that function, of course, is 4x to the third...