Question: If a rod lies along the x-axis between a and b, the moment of the rod is a∫b xδ(x)dx, where δ(x) is its density in grams/meter at a position x meters. Find the moment and center of mass of the rod in Problem.
Problem: A rod has length 2 meters. At a distance x meters from its left end, the density of the rod is given by
δ(x) = 2 + 6x gm/m.
(a) Write a Riemann sum approximating the total mass of the rod.
(b) Find the exact mass by converting the sum into an integral.