Given #f:[0,1]->RR# an integrable function such that #int_0^1f(x)dx=int_0^1 xf(x)dx= 1# prove that #int_0^1f(x)^2dx ge 4#?
1 Answer
Oct 28, 2016
so
Explanation:
Just think that
Then find a and b that maximize
Calculate gradient and put it = 0. You obtain