If-a-continuous-function-f-R-R-satisfies-0-1-f-x-dx-0-1-xf-x-dx-1-prove-that-0-1-f-x-2-dx-4-

Question Number 120089 by ZiYangLee last updated on 29/Oct/20

If a continuous function f : R \to R satisfies

\int_{0}^{1} f (x) d x = \int_{0}^{1} x f (x) d x = 1

prove that \int_{0}^{1} {(f (x))}^{2} d x ⩾ 4