Question

How prove $\frac{\int_{0}^{1}xf^2(x)dx}{\int_{0}^{1}xf(x)dx}\le\frac{\int_{0}^{1}f^2(x)dx}{\int_{0}^{1}f(x)dx}$

score 344 · Answer 1 · 2026-04-16 20:18:55

344

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How prove $\frac{\int_{0}^{1}xf^2(x)dx}{\int_{0}^{1}xf(x)dx}\le\frac{\int_{0}^{1}f^2(x)dx}{\int_{0}^{1}f(x)dx}$

Published on 16 Apr 2026 - 20:18

score 2k · Answer 2 · 2026-04-11 18:11:29

2k

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Jensen integral inequality in multidimensional case

Published on 11 Apr 2026 - 18:11

score 47.9k · Answer 3 · 2026-04-16 17:53:25

47.9k

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Integral Inequality Absolute Value: $\left| \int_{a}^{b} f(x) g(x) \ dx \right| \leq \int_{a}^{b} |f(x)|\cdot |g(x)| \ dx$

Published on 16 Apr 2026 - 17:53

score 67 · Answer 4 · 2026-04-09 06:03:44

67

Views

A Expectation question

Published on 09 Apr 2026 - 6:03

score 262 · Answer 5 · 2026-04-09 22:57:08

262

Views

Simplification of integral with division between summations

Published on 09 Apr 2026 - 22:57

score 230 · Answer 6 · 2026-04-08 20:37:59

230

Views

An integral inequality.

Published on 08 Apr 2026 - 20:37

score 105 · Answer 7 · 2026-04-08 20:37:57

105

Views

An inequality-Is it possible?

Published on 08 Apr 2026 - 20:37

score 1.2k · Answer 8 · 2026-04-15 19:18:37

1.2k

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Riemann integrable functions: $\left|\int_a^bf(x)\,\mathrm dx\right|\le\int_a^b|f(x)|\,\mathrm dx$

Published on 15 Apr 2026 - 19:18

score 944 · Answer 9 · 2026-03-26 20:25:45

944

Views

How to prove equality from poincare inequality?

Published on 26 Mar 2026 - 20:25

score 364 · Answer 10 · 2026-04-14 19:39:47

364

Views

Prove that $\int_{0}^{1}|f(x)f'(x)|dx\leq\frac{1}{2}\int_{0}^{1}|f'(x)|^2dx$

Published on 14 Apr 2026 - 19:39

score 293 · Answer 11 · 2026-04-10 17:45:42

293

Views

Integral inequality

Published on 10 Apr 2026 - 17:45

score 119 · Answer 12 · 2026-04-13 21:00:45

119

Views

Proof that $E[\exp(|A|)] \leq \exp(\delta) + \exp(\delta)P(|A|>\delta) + \int_\delta^\infty\exp(x)P(|A|>x)dx$

Published on 13 Apr 2026 - 21:00

score 502 · Answer 13 · 2026-04-14 13:29:59

502

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If the weighted $L^p$ norm of a measurable function is finite, is the weighted $L^p$ norm of the antiderivative also finite?

Published on 14 Apr 2026 - 13:29

score 88 · Answer 14 · 2026-04-15 00:14:47

88

Views

A certain interpolation inequality

Published on 15 Apr 2026 - 0:14

score 329 · Answer 15 · 2026-04-09 12:54:29

329

Views

inequality with sup and Expectations

Published on 09 Apr 2026 - 12:54

List Question

How prove $\frac{\int_{0}^{1}xf^2(x)dx}{\int_{0}^{1}xf(x)dx}\le\frac{\int_{0}^{1}f^2(x)dx}{\int_{0}^{1}f(x)dx}$

Jensen integral inequality in multidimensional case

Integral Inequality Absolute Value: $\left| \int_{a}^{b} f(x) g(x) \ dx \right| \leq \int_{a}^{b} |f(x)|\cdot |g(x)| \ dx$

A Expectation question

Simplification of integral with division between summations

An integral inequality.

An inequality-Is it possible?

Riemann integrable functions: $\left|\int_a^bf(x)\,\mathrm dx\right|\le\int_a^b|f(x)|\,\mathrm dx$

How to prove equality from poincare inequality?

Prove that $\int_{0}^{1}|f(x)f'(x)|dx\leq\frac{1}{2}\int_{0}^{1}|f'(x)|^2dx$

Integral inequality

Proof that $E[\exp(|A|)] \leq \exp(\delta) + \exp(\delta)P(|A|>\delta) + \int_\delta^\infty\exp(x)P(|A|>x)dx$

If the weighted $L^p$ norm of a measurable function is finite, is the weighted $L^p$ norm of the antiderivative also finite?

A certain interpolation inequality

inequality with sup and Expectations

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