A thin onedimensional wire of constant density is bent into

A thin (one-dimensional) wire of constant density is bent into the shape of a semicircle of radius a. Find the location of its center of mass. Assume the origin is at the midpoint of the diameter with the y-axis pointing up. Assume the density is one. Using polar coordinates, determine the integral to be used to most efficiently find the moment with respect to the x-axis, M_x. Use increasing limits of integration.

Solution