MathDB
Today's calculation of Integral 152

Source: Fukui University entrance exam/Engineering 1970

September 6, 2006
calculusintegrationfunctioncalculus computations

Problem Statement

Let f(x)f(x) the function such that f(0)=0, ∣f′(x)∣≤11+x (x≥0).f(0)=0,\ |f'(x)|\leq \frac{1}{1+x}\ (x\geq 0). Prove that ∫0e−1{f(x)}2dx≤e−2.\int_{0}^{e-1}\{f(x)\}^{2}dx\leq e-2.
Back to ProblemsView on AoPS