MathCastle
PutnamSuperchallengeIntegrals I: Feynman's Trick

Integrals I: Feynman's Trick · Superchallenge problem

A function f:R→Rf:\mathbb R\to\mathbb R satisfies f(x+y)=f(x)+f(y)+xyf(x+y) = f(x) + f(y) + xy for all real x,yx, y, and f(1)=1f(1) = 1. Compute f(10)f(10).