https://youtu.be/x9u3idxKMrc

In this video I go over a pretty extensive example on determining the arc length of a curve but this time determine it as a function of x. This allows the ability to measure the length of a curve from a given point up to any point on the curve. The arc length function in this example is determined for the curve y = x^2 - 1/8*ln(x) from the starting point (1, 1).

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# Applications of Integrals: Arc Length: Example 4

Find the arc length function for the following function by taking the point P<sub>0</sub>(1, 1) as the starting point:

![](https://cdn.steemitimages.com/DQmdUQFEwZrQ7o7do5CgVShVAQ83bNg3FXjbY8iVfwn2Pow/image.png)

![](https://cdn.steemitimages.com/DQmfBuscpdFJDPSn6sZLdbfmdcM46zwd3d9Wtf39XxccgXQ/image.png)

![](https://cdn.steemitimages.com/DQmTjPdbhsRMzSZCs6nhXk965AHezUfFti1WSsi6RKYCLms/image.png)

![](https://cdn.steemitimages.com/DQmchTodrE93NYy8DceD14eUe3jKp1AbXhXZxqq11srpNiY/image.png)