The problem of finding the center of mass by integral of unary function in higher mathematics

There is nothing wrong with what the landlord said, indeed:

X static moment should be the sum of the product of the mass of each mass element and the Y coordinate of the mass element: Mx=∑ mi * yi (i= 1 to n).

1. On the narrow rectangle shown in the figure, the y coordinate of the center of mass is the midpoint coordinate of the narrow rectangle, namely:

y = (y？ + y？ )/ 2 = [f(x) + g(x)] / 2

2. The micro-area of this long and narrow rectangle is dA = [f(x)-g(x)] dx.

3. The micro-mass of this long and narrow rectangle DM = [f (x)-g (x)] dx×1= [f (x)-g (x)] dx.

4. The minute torque of this long and narrow rectangle DMX = [f (x)-g (x)] dx× y.

= [f(x) - g(x)] dx × [f(x) + g(x)] / 2

= ? [f(x) - g(x)] × [f(x) + g(x)] dx

Welcome questions.