Chebyshev Integral Inequality

Chebyshev Integral Inequality

If $$f$$ and $$g$$ are similarly ordered on $$[a,b]$$, then:

$$\frac{1}{b-a}\int_a^bf(x)g(x)\,dx\geq\left(\frac{1}{b-a}\int_a^bf(x)\,dx\right)\left(\frac{1}{b-a}\int_a^bg(x)\,dx\right)$$

Usage

- Used in advanced inequalities involving integrals of similarly ordered functions.