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.

Assuming the region is of uniform density, compute the mass of the region and its moments.

If n > m, then in the interval [0, 1] we have f(x) ≤ g(x). This means the mass is

The moments are

Then the centroid is

equal to

step-by-step explanation:

24/56=hx^7

step-by-step explanation: