Ampere's law with NON-Uniform Current Density

Here is an example of how to do a worst case scenario with Ampere's law (for a long, straight wire): A NON-uniform current density flowing through the cross sectional area of the wire.

Current density is just the current / (cross sectional area the current flows through). If this flow is a function of the radius, then it is NON-uniform flow, and, like a non-uniform charge density for Gauss's law, we will need to integrate the current density function to find the current inside the region we want. It hopefully sounds worse than it is, so check out the video for an example. I hope it helps!