Question-169242

Question Number 169242 by Skabetix last updated on 26/Apr/22

Answered by Skabetix last updated on 26/Apr/22

p l e a s e h e l p

Answered by kowalsky78 last updated on 26/Apr/22

I f f i s c o n t i n o u s i n [0, 1], \exists M \in ℜ s u c h t h a t ∣ f (x) ∣⩽ M . S o,

∣ \int_{0}^{1} x^{n} f (x) d x ∣⩽ \int_{0}^{1} x^{n} ∣ f (x) ∣ d x ⩽ M \int_{0}^{1} x^{n} d x = \frac{M}{n + 1}

I f w e t a k e t h e l i m i t w e h a v e

l i \underset{n \to + \infty}{m} \int_{0}^{1} x^{n} f (x) d x = 0

Commented by Skabetix last updated on 26/Apr/22

t h a n k y o u s i r