Today's calculation of Integral 356
Source: 1982 Hirosaki University entrance exam/Physics, Chemistry, Earth Science
July 2, 2008
calculusintegrationfunctioncalculus computations
Problem Statement
A continuous function satisfies that \frac {d}{dx}\left(\int_0^x f(x \plus{} t)\ dt \right)\equal{} 0. Find the necessary and sufficient condition such that \sum_{n \equal{} 1}^{\infty} f(2^n) \equal{} 1.