### 4th Putnam 1941

**Problem A6**

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**

4th Putnam 1941

© John Scholes

jscholes@kalva.demon.co.uk

5 Mar 2002