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 341 · Answer 1 · 2013-06-19 06:01:01

341

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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 19 Jun 2013 - 6:01

score 2k · Answer 2 · 2013-06-22 18:12:30

2k

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Jensen integral inequality in multidimensional case

Published on 22 Jun 2013 - 18:12

score 47.9k · Answer 3 · 2013-06-25 16:26:09

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 25 Jun 2013 - 16:26

score 64 · Answer 4 · 2013-06-28 22:52:41

64

Views

A Expectation question

Published on 28 Jun 2013 - 22:52

score 259 · Answer 5 · 2013-07-04 20:02:10

259

Views

Simplification of integral with division between summations

Published on 04 Jul 2013 - 20:02

score 227 · Answer 6 · 2013-07-13 14:00:16

227

Views

An integral inequality.

Published on 13 Jul 2013 - 14:00

score 102 · Answer 7 · 2013-07-14 08:20:14

102

Views

An inequality-Is it possible?

Published on 14 Jul 2013 - 8:20

score 1.2k · Answer 8 · 2013-07-19 15:17:31

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 19 Jul 2013 - 15:17

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 362 · Answer 10 · 2013-07-28 20:46:25

362

Views

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

Published on 28 Jul 2013 - 20:46

score 290 · Answer 11 · 2013-08-07 05:24:47

290

Views

Integral inequality

Published on 07 Aug 2013 - 5:24

score 116 · Answer 12 · 2013-08-16 15:38:31

116

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 16 Aug 2013 - 15:38

score 500 · Answer 13 · 2013-08-28 15:39:24

500

Views

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 28 Aug 2013 - 15:39

score 85 · Answer 14 · 2013-09-03 21:06:03

85

Views

A certain interpolation inequality

Published on 03 Sep 2013 - 21:06

score 326 · Answer 15 · 2013-09-05 10:48:05

326

Views

inequality with sup and Expectations

Published on 05 Sep 2013 - 10:48

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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