设 $fin C[0,1]$ 适合 $$ex int_x^1 f(t) d tgeq frac{1-x^2}{2},quad forall xin [0,1]. eex$$ 试证: $$ex int_0^1 f^2(t) d tgeq frac{1}{3}. eex$$
设 $fin C[0,1]$ 适合 $$ex int_x^1 f(t) d tgeq frac{1-x^2}{2},quad forall xin [0,1]. eex$$ 试证: $$ex int_0^1 f^2(t) d tgeq frac{1}{3}. eex$$