f is defined for the non-negative reals and takes positive real values. The centroid of the area lying under the curve y = f(x) between x = 0 and x = a has x-coordinate g(a). Prove that for some positive constant k, f(x) = k g'(x)/(x - g(x))2 e ∫ 1/(t - g(t)) dt.
Solution
© John Scholes
jscholes@kalva.demon.co.uk
5 Mar 2002