Consider the functions f(x) = xn and g(x) = xm on the interval [0, 1], where m and n are positive integers and n > m. Find the centroid of the region bounded by f and g.

Find the centroid of the region bounded by the graphs of y = xe (e is raised to the power -x/2 ) , y = 0 , x = 0 , x = 4

The centroid of the plane region bounded by the graphs of y = f(x), y = 0, x = 0, and x = 3 is (1.2, 1.4). Without integrating, find the centroid of each of the regions bounded by the graphs of the following sets of equations. Explain your reasoning. (a) y = f(x) + 2, y = 2, x = 0, and x = 3 (b) y = f(x − 2), y = 0, x = 2, and x = 5 (c) y = −f(x), y = 0, x = 0, and x = 3