Integral inequality $\int_{0}^{1}f^2\left(x\right)dx\geq\frac{3}{13}$
97643
Prove that:$f(f(x)) = x^2 \implies \int_{0}^{1}{(f(x))^2dx} \geq \frac{3}{13}$
118884
The sine inequality $\frac2\pi x \le \sin x \le x$ for $0<x<\frac\pi2$
95266
Show $|t|\leq \pi \Rightarrow |e^{it}-1|\geq 2|t|/ \pi$
95626
$\int_X |f_n - f| \,dm \leq \frac{1}{n^2}$ for all $n \geq 1$ $\implies$ $f_n \rightarrow f$ a.e.
156599
Wirtinger Inequality: $\int_0^1 f'^2 \geq \pi^2 \int_0^1 f^2 $
34907
Show that $\int_{0}^{1}\{P(x)\}^{2}\,dx = (n + 1)^{2}\left(\int_{0}^{1}P(x)\,dx\right)^{2}$
4656
Prove that there is a $\delta$ such that $\int_{0}^{1} (f(x))^2dx\leq \delta$$\int_{0}^{1} (f'(x))^2dx$ for all $f$ with these conditions
137614
$\left|\frac{x}{|x|}-\frac{y}{|y|}\right|\leq |x-y|$, for $|x|, |y|\geq 1$?
53748
Find maximum value of $\int_{0}^{1}\left(f(x)\right)^3dx$
117046
Show that $\frac{a^2}{\sqrt{(1+a^3)(1+b^3)}}+\frac{b^2}{\sqrt{(1+b^3)(1+c^3)}}+\frac{c^2}{\sqrt{(1+c^3)(1+a^3)}} \geq \frac{4}{3}$
100869
How to show that $\int_0^1 \left(\sqrt[3]{1-x^7} - \sqrt[7]{1-x^3}\right)\;dx = 0$
107601
Use of inequality $1 - \cos (x) \leq x^2 /2$
85763
Inequality $(1+\frac1k)^k \leq 3$
44233
How to prove this inequality $ x + \frac{1}{x} \geq 2 $
102019
How to solve inequality $1-\frac{1}{x}\geq 0$ correctly?
26962
Proving an inequality involving the logarithm function: $\frac{1}{n+1} \leq \ln \left(1+\frac 1n\right) \leq \frac 1n$
34398
Prove $\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$