let-f-C-0-0-pi-R-prove-that-lim-n-0-pi-f-x-sin-nx-dx-2-pi-0-pi-f-x-dx-

Question Number 36932 by maxmathsup by imad last updated on 07/Jun/18

l e t f \in C^{0} ([0, π], R) p r o v e t h a t

{l i m}_{n \to + \infty} \int_{0}^{π} f (x) ∣ s i n (n x) ∣ d x = \frac{2}{π} \int_{0}^{π} f (x) d x .