00:01
The problem i will be working on today is this one.
00:04
Use the arc length formula to find the length of the curve y equals the square root of 2 minus x squared over the interval from 0 to 1.
00:15
So from 0 to 1 we're finding this arc length.
00:21
And then we're going to check our answer by noticing that this is part of a circle and so we're going to solve it just a little bit differently.
00:31
So when i start doing a problem for the first time, especially if i learn a new formula, i write it down.
00:40
So the arc length is equal to the integral over the interval a to b the square root of 1 plus the first derivative squared dx.
00:50
I write it down so that i become familiar with it.
00:53
So i need the first derivative.
00:54
So the first derivative of our function is going to be 1 half times 2 minus x squared to the negative 1 half times negative 2x.
01:02
Don't forget the negative 2x from the chain rule.
01:05
And so you've got this as your first derivative.
01:11
I don't need to simplify just yet.
01:13
We're just going to hang on to that one.
01:17
Okay now that we've found the first derivative, we're going to substitute that into our formula here...