So now we want to find the mass of a rod where we know the linear density. So we're imagining we have some sort of, perhaps, metal rod where because of the way it was constructed, the density of the material depends upon the location on the rod. So for example, if this measurement is x, we're saying that at this point right here, at this x value, we know the density of the function somehow. So maybe we know the density is 8 minus x, rams per centimeter. So this is a linear density. A density is a mass per unit measurement. Sometimes you have linear densities, which is a mass per length, sometimes you have area densities, mass per an area, sometimes you have volume densities. In this case, we have a linear density. So suppose that this entire rod was 6 centimeters long. Then this is telling me at the very beginning, this end is very, very heavy mass. There's 8 grams per centimeter down on this end. We're on this end. The mass is decreased down only 2 grams per centimeter. So we want to know what is the total mass of the rod and the difficulty is the mass is constant. So what we do is what we do in all cases like this is we slice it up into tiny little bits where on each bit the density will essentially be constant. So we're going to chop this rod up into a bunch of tiny little pieces of rod, each of which will have length dx. So if a piece of rod has a length dx, what is the mass of this tiny little piece? Well, we know the density. The density is 8 minus 6 grams per centimeter. For any given x value, that will be the density. And we know the length of the slice of the piece is dx centimeters. The centimeters cancel. This gives us the mass of that piece. To find the total mass of the rod, we're going to add up all those little pieces. So that's the mass of one piece. We're going to add up all the pieces from the start of the rod to the end of the rod. And that's going to give us the total mass of this rod.