New posts in integral-inequality

$\int_a^bf^2(x)\,dx\le \frac{2}{3}\int_a^bf(x)\,dx$ for a convex differentiable function

Integral Inequality $|\int_0^x f(t)dt|\le \frac{2}{81}\max_{0\le x\le1}|f^{''}(x)|$

How prove this $\left(\int_{-\pi}^{\pi}f(x)\sin{x}dx\right)^2+\left(\int_{-\pi}^{\pi}f(x)\cos{x}dx\right)^2\le\frac{\pi}{2}\int_{-\pi}^{+\pi}f^2(x)dx$

Prove an integral inequality $|\int\limits_0^1f(x)dx|\leq\frac{1-a+b}{4}M$ [closed]

How to prove Cauchy-Schwarz integral inequality?

Is this function decreasing in $x$?

Show inequality of integrals (cauchy-schwarz??)

Prove $1.43 < \int_0^1 e^{x^2}\,\mathrm{d}x < \frac{e+1}{2}$

$L^2$ norm and $L^{\infty}$ inequality for periodic smooth functions

Prove the following integral inequality: $\int_{0}^{1}(f''(x))^2dx\ge 1920\left(\int_{0}^{1}f(x)dx\right)^2$

A problem from the Shortlist of the Romanian Mathematics Olympiad

Prove Friedrichs' inequality

Prove that $f(1)-f(1/e)\le \int_0^1 \sqrt{x} f'(x) dx$

Which conditions must fulfill $f(t)$ to have an absolute-integrable Fourier Transform $F(w)$: $\int\limits_{-\infty}^\infty |F(w)| dw < \infty$?

How prove this integral inequality $\int_{0}^{s}f(x)\,dx\le\int_{s}^{1}f(x)\,dx\le\dfrac{s}{1-s}\int_{0}^{s}f(x)\,dx$

How to prove $\int_0^1 f^2(x)\cdot f'^4(x)\ dx\leq \int_0^1 f^4(x)\cdot f''^2(x)\ dx$ [closed]

How to prove that there exists $g(x)$ such $\int_{0}^{1}g(x)dx\ge\frac{1}{2}\int_{0}^{1}f(x)dx$

How prove this $\int_{a}^{b}[f''(x)]^2dx\ge\dfrac{4}{b-a}$

How to prove that $\frac{2}{\pi}\int_{x}^{px}\left(\frac{\sin{t}}{t}\right)^2\,\mathrm dt\le 1-\dfrac{1}{p}$ for $p >1, x\ge0$

Prove that $\int_a^bxf(x)dx\geq\frac{b+a}{2}\int_a^bf(x)dx$