known-function-f-diferensiable-continues-at-a-b-If-f-a-f-b-0-and-a-b-f-x-2-dx-1-Prove-that-a-b-x-2-f-x-2-dx-1-4-

Question Number 55643 by gunawan last updated on 01/Mar/19

known function f

diferensiable continues at [a, b]

If f (a) = f (b) = 0

and

\int_{a}^{b} {[f (x)]}^{2} d x = 1

Prove that

\int_{a}^{b} x^{2} {[f^{'} (x)]}^{2} d x ⩾ \frac{1}{4}

Commented by tanmay.chaudhury50@gmail.com last updated on 01/Mar/19

[f (x)] \leftarrow i s [.] g r e a t e s t i n t e g e r f u n c t i o n o r

s i m p l y b r a c k e t \dots