MathDB

If the

x

-coordinate

\overline{x}

of the center of mass of the area lying between the

x

-axis and the curve

y=f(x)

with

f(x)>0

, and between the lines

x=0

and

x=a

is given by

\overline{x}=g(a),

show that

f(x)=A\cdot \frac{g'(x)}{(x-g(x))^{2}} \cdot e^{\int \frac{1}{t-g(t)} dt},

where

A

is a positive constant.

Problem Statement