Question

How to prove the inequalities $\int_{0}^{1}\sin{(x^n)}dx\ge\int_{0}^{1}(\sin x)^ndx\ge 0$

score 162 · Answer 1 · 2014-05-04 10:18:51

162

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How to prove the inequalities $\int_{0}^{1}\sin{(x^n)}dx\ge\int_{0}^{1}(\sin x)^ndx\ge 0$

Published on 04 May 2014 - 10:18

score 295 · Answer 2 · 2014-05-08 15:00:32

295

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How find the minimum of the value $k$ such this intergral $\int_{0}^{1}f^2(x)dx\le k\left(\int_{0}^{1}f(x)dx\right)^2$

Published on 08 May 2014 - 15:00

score 76 · Answer 3 · 2014-05-08 21:23:25

76

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Reference for theorem? Inequality of integrals of increasing function over two distributions

Published on 08 May 2014 - 21:23

score 243 · Answer 4 · 2014-05-11 03:48:39

243

Views

Integral inequality for nonnegative functions

Published on 11 May 2014 - 3:48

score 167 · Answer 5 · 2014-05-13 06:13:47

167

Views

Inequalities giving incorrect solution

Published on 13 May 2014 - 6:13

score 81 · Answer 6 · 2014-05-19 18:39:11

81

Views

If $f$ is $2 \pi$ periodic and $\int_{0}^{2 \pi} f(t) dt=0$ then $\int_{0}^{2 \pi} (f(t))^2 dt \le \int_{0}^{2 \pi} (f'(t))^2 dt$

Published on 19 May 2014 - 18:39

score 771 · Answer 7 · 2026-03-25 07:53:19

771

Views

Upper bound of difference of squares of quantile standard normal

Published on 25 Mar 2026 - 7:53

score 179 · Answer 8 · 2014-05-22 04:39:36

179

Views

How can we prove this integral inequality ? $\int_{0}^{\frac{\pi}{2}}\left|\frac{\sin{(2n+1)t}}{\sin{t}}\right|dt<\pi\left(1+\frac{\ln{n}}{2}\right)$

Published on 22 May 2014 - 4:39

score 138 · Answer 9 · 2014-05-23 08:52:46

138

Views

How prove this inequality $I=\int_{0}^{\sqrt{2\pi}}\sin{x^2}dx>0$

Published on 23 May 2014 - 8:52

score 150 · Answer 10 · 2014-05-29 01:05:02

150

Views

Integrals on a closed ball

Published on 29 May 2014 - 1:05

score 78 · Answer 11 · 2014-05-31 11:53:51

78

Views

estimating $L^p$ norm of $\frac{x}{|x|^3} \ast (-\text{div}_x \ldots)$

Published on 31 May 2014 - 11:53

score 96 · Answer 12 · 2014-06-02 13:29:16

96

Views

How to prove this ${\pi\over4}\leq\int_0^{\pi\over2}e^{-\sin^2{x}}dx\leq{11\over32}\pi$

Published on 02 Jun 2014 - 13:29

score 194 · Answer 13 · 2014-06-11 20:58:08

194

Views

Reference for $f \in L^{p,\infty} \cap L^{q}$ then $f \in L^r$ for $p < r \leq q$

Published on 11 Jun 2014 - 20:58

score 229 · Answer 14 · 2014-06-14 06:46:31

229

Views

An Integral Inequality Problem

Published on 14 Jun 2014 - 6:46

score 483 · Answer 15 · 2014-06-21 19:47:44

483

Views

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

Published on 21 Jun 2014 - 19:47

List Question

How to prove the inequalities $\int_{0}^{1}\sin{(x^n)}dx\ge\int_{0}^{1}(\sin x)^ndx\ge 0$

How find the minimum of the value $k$ such this intergral $\int_{0}^{1}f^2(x)dx\le k\left(\int_{0}^{1}f(x)dx\right)^2$

Reference for theorem? Inequality of integrals of increasing function over two distributions

Integral inequality for nonnegative functions

Inequalities giving incorrect solution

If $f$ is $2 \pi$ periodic and $\int_{0}^{2 \pi} f(t) dt=0$ then $\int_{0}^{2 \pi} (f(t))^2 dt \le \int_{0}^{2 \pi} (f'(t))^2 dt$

Upper bound of difference of squares of quantile standard normal

How can we prove this integral inequality ? $\int_{0}^{\frac{\pi}{2}}\left|\frac{\sin{(2n+1)t}}{\sin{t}}\right|dt<\pi\left(1+\frac{\ln{n}}{2}\right)$

How prove this inequality $I=\int_{0}^{\sqrt{2\pi}}\sin{x^2}dx>0$

Integrals on a closed ball

estimating $L^p$ norm of $\frac{x}{|x|^3} \ast (-\text{div}_x \ldots)$

How to prove this ${\pi\over4}\leq\int_0^{\pi\over2}e^{-\sin^2{x}}dx\leq{11\over32}\pi$

Reference for $f \in L^{p,\infty} \cap L^{q}$ then $f \in L^r$ for $p < r \leq q$

An Integral Inequality Problem

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

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