Moment of Inertia with a NON-UNIFORM linear mass density....YIKES!!

Things don't usually seem promising when you hear phrases like, "non-uniform linear mass density!" That just sounds nasty difficult! But if you step back and give it a chance, it allows us to look at objects other than just, say, nice neat sticks like a meterstick, that is uniform....the mass is distributed evenly along the length of the stick, with the center of mass at the actual center of the stick. But what about something like a baseball bat, where the mass per unit length changes along the stick, as it gets wider and heavier on one side compared to the skinny side. The center of mass of a baseball bat is not at the actual middle of the bat.

Linear mass density is the ratio of Mass/Length, or M/L (the symbol is lambda). We use this ratio when we calculate the integral for the moment of inertia of a stick. But what if we want to set things up for the baseball bat? How do we find the moment of inertia for a non-uniform stick? This video shows an example, which comes from the 2018 AP exam.