(862, #13) A lamina occupies the part of the disk x^2 + y^2 <= 1 in the first quadrant. Find its center of mass if the density at any point is proportional to its distance from the x-axis.

Solution: The phrase "the density at any point is proportional to its distance from the x-axis" means that where k is some constant.

Setting up the integral and then switching to polar coordinates we have

Next,

Finally,

MapleCode