The figure shows a shaded area, bounded by the parabola y = kx² and the x-axis. a. Calculate the value of k. b. Find the x- and y-coordinates of the area's centroid. c. If the area has an area density of o = 7xy kg/m², find the x- and y-coordinates of its center of mass. d. Compute the distance between the area's centroid and its center of mass.

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Center of Gravity and Centroid

The term center of gravity indicates the position or location of a point about which the whole weight of a body or system is supposed to be concentrated, which means the whole weight of the body or system works through this point. It is closely related to mass distribution. For all positions of the body, the center of gravity would be a single point.