MathDB

4

Part of 1980 Swedish Mathematical Competition

Problems(1)

int f(x)g(x) dx <= int f(x)g(1-x) dx

Source: 1980 Swedish Mathematical Competition p4

3/28/2021
The functions ff and gg are positive and continuous. ff is increasing and gg is decreasing. Show that ∫01f(x)g(x)dx≤∫01f(x)g(1−x)dx \int\limits_0^1 f(x)g(x) dx \leq \int\limits_0^1 f(x)g(1-x) dx
integrationanalysisinequalities