Recent content by Integration1

Thank you so much for inspiration. Maybe using the convex function - \ln (x) would solve the problem? Another question: How can i deduce the integral from of Jensen's inequality from the finite one? Cause I have only learned the latter one

Let f(x) \in C[a,b] and let f(x)>0 on [a,b]. Prove that \exp \Big(\frac{1}{b-a}\int_a^b \ln f(x) dx \Big)\leq \frac{1}{b-a}\int_a^b f(x) dx I have learned Gronwall's Inequality and Jensen's Inequality(and inequality deduced from it like Cauchy Schwarz Inequality) but i couldn't use them to...