Newbetuts

Show $\int_{0}^{1}(\int_{0}^{x}g(t)dt)^2 dx\leq\frac{1}{2}\int_0^1(1-x^2)(g(x))^2 dx$ for any $g(x)$ continuous

Does $||f'||_\infty \leq \sqrt{t_F-t_0}\,||f'||_2$ hold for time-limited continuous functions $f(t)$ with $\sup_t |f'(t)|<\infty$?

Hilbert's Inequality

Prove that $\int\limits_0^1 \bigg | \frac{f''(x)}{f(x)} \bigg| dx \ge \frac{4(M-1)}{M}$

Inequality of integrals $\int_0^1(f(x))^2 dx \geq 4$ if $\int_0^1xf(x) dx=\int_0^1f(x) dx = 1$

How to prove this integral inequality $ \int_0^{2\pi} p(x)[p(x)+p''(x)] dx \int_0^{2\pi}\frac{1}{p(x)+p''(x)} dx\geq 2\pi \int _0^{2\pi} p(x) dx $?

Maximum of a Function Bounded by Average of Integral and Integral of Derivative [duplicate]

Given $\int_{\frac13}^{\frac23}f(x)dx=0$, how to prove $4860(\int_0^1f(x)dx)^2\le 11\int_0^1|f''(x)|^2dx$?

Inequality of numerical integration $\int _0^\infty x^{-x}\,dx$.

Prove $\int _0^\infty f^2 dx \leq \cdots $ for $f$ convex

Proof of bound on $\int t\,f(t)\ dt$ given well-behaved $f$

Alternative proof of simple integral inequality

Prove that $\int_0^1 \big(1-x^2\big) \big(f'(x)\big)^2\,dx \ge 24 \left(\int_0^1 xf(x)\,dx\right)^{\!2}$

Holder's inequality for infinite products

$|f(x)|\leq \sqrt{\frac{\pi}{3}\int_0^\pi f'^2}$

New posts in integral-inequality

Show $\int_{0}^{1}(\int_{0}^{x}g(t)dt)^2 dx\leq\frac{1}{2}\int_0^1(1-x^2)(g(x))^2 dx$ for any $g(x)$ continuous

Easier ways to prove $\int_0^1 \frac{\log^2 x-2}{x^x}dx<0$

Nonnegativity of integral, integral operator

An inequality from the handbook of mathematical functions (by Abramowitz and Stegun)

How prove this integral inequality $\int_{0}^{1}f^2(x)dx\ge 24\left(\int_{0}^{1}f(x)dx\right)^2$?

Is the Riemann integral of a strictly smaller function strictly smaller?

Does $||f'||_\infty \leq \sqrt{t_F-t_0}\,||f'||_2$ hold for time-limited continuous functions $f(t)$ with $\sup_t |f'(t)|<\infty$?

Hilbert's Inequality

Prove that $\int\limits_0^1 \bigg | \frac{f''(x)}{f(x)} \bigg| dx \ge \frac{4(M-1)}{M}$

Inequality of integrals $\int_0^1(f(x))^2 dx \geq 4$ if $\int_0^1xf(x) dx=\int_0^1f(x) dx = 1$

How to prove this integral inequality $ \int_0^{2\pi} p(x)[p(x)+p''(x)] dx \int_0^{2\pi}\frac{1}{p(x)+p''(x)} dx\geq 2\pi \int _0^{2\pi} p(x) dx $?

Maximum of a Function Bounded by Average of Integral and Integral of Derivative [duplicate]

Given $\int_{\frac13}^{\frac23}f(x)dx=0$, how to prove $4860(\int_0^1f(x)dx)^2\le 11\int_0^1|f''(x)|^2dx$?

Inequality of numerical integration $\int _0^\infty x^{-x}\,dx$.

Prove $\int _0^\infty f^2 dx \leq \cdots $ for $f$ convex

Proof of bound on $\int t\,f(t)\ dt$ given well-behaved $f$

Alternative proof of simple integral inequality

Prove that $\int_0^1 \big(1-x^2\big) \big(f'(x)\big)^2\,dx \ge 24 \left(\int_0^1 xf(x)\,dx\right)^{\!2}$

Holder's inequality for infinite products

$|f(x)|\leq \sqrt{\frac{\pi}{3}\int_0^\pi f'^2}$