Question

How show that $\dfrac{a^3}{3}\ge\int_{0}^{a}|F(x)-x|^2dx$

score 187 · Answer 1 · 2013-04-27 08:34:45

187

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How show that $\dfrac{a^3}{3}\ge\int_{0}^{a}|F(x)-x|^2dx$

Published on 27 Apr 2013 - 8:34

score 105 · Answer 2 · 2013-04-29 20:59:05

105

Views

The integral $\int_0^1\dfrac{(-x)^n}{1+x} dx $

Published on 29 Apr 2013 - 20:59

score 803 · Answer 3 · 2013-05-04 17:21:10

803

Views

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

Published on 04 May 2013 - 17:21

score 768 · Answer 4 · 2013-05-09 14:30:04

768

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

Published on 09 May 2013 - 14:30

score 1.3k · Answer 5 · 2013-05-10 16:44:24

1.3k

Views

Prove $\int_0^{\infty } \frac{1}{\sqrt{6 x^3+6 x+9}} \, dx=\int_0^{\infty } \frac{1}{\sqrt{9 x^3+4 x+4}} \, dx$

Published on 10 May 2013 - 16:44

score 274 · Answer 6 · 2013-05-14 14:41:41

274

Views

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

Published on 14 May 2013 - 14:41

score 2k · Answer 7 · 2013-05-14 18:51:33

2k

Views

Proof of Schur's test via Young's inequality

Published on 14 May 2013 - 18:51

score 724 · Answer 8 · 2013-05-15 11:59:09

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 $p >1, x\ge0$

score 322 · Answer 9 · 2013-05-23 06:38:00

322

Views

Prove with integration the inequality $e(\frac{n}{e})^n < n! < n \times e(\frac{n}{e})^n$

Published on 23 May 2013 - 6:38

score 427 · Answer 10 · 2013-05-25 12:42:23

427

Views

Inductively prove that this sequence of integrals is bounded.

Published on 25 May 2013 - 12:42

score 482 · Answer 11 · 2013-06-05 15:01:22

482

Views

prove this $\int_{0}^{2}f^2(x)dx\le\int_{0}^{2}f'^2(x)dx$

Published on 05 Jun 2013 - 15:01

score 463 · Answer 12 · 2013-06-05 15:41:43

463

Views

Cauchy inequality $\Rightarrow$ Schwarz's integral inequality. Why can't the limit of the prior be used to deduce the latter?

Published on 05 Jun 2013 - 15:41

score 974 · Answer 13 · 2013-06-06 02:14:24

974

Views

Inequality for sums of reciprocals

Published on 06 Jun 2013 - 2:14

score 143 · Answer 14 · 2013-06-09 17:18:39

143

Views

Exercice on periodic function

Published on 09 Jun 2013 - 17:18

score 810 · Answer 15 · 2013-06-13 03:39:22

810

Views

integral inequality with derivative

Published on 13 Jun 2013 - 3:39

List Question

How show that $\dfrac{a^3}{3}\ge\int_{0}^{a}|F(x)-x|^2dx$

The integral $\int_0^1\dfrac{(-x)^n}{1+x} dx $

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

Prove $\int_0^{\infty } \frac{1}{\sqrt{6 x^3+6 x+9}} \, dx=\int_0^{\infty } \frac{1}{\sqrt{9 x^3+4 x+4}} \, dx$

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

Proof of Schur's test via Young's inequality

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 with integration the inequality $e(\frac{n}{e})^n < n! < n \times e(\frac{n}{e})^n$

Inductively prove that this sequence of integrals is bounded.

prove this $\int_{0}^{2}f^2(x)dx\le\int_{0}^{2}f'^2(x)dx$

Cauchy inequality $\Rightarrow$ Schwarz's integral inequality. Why can't the limit of the prior be used to deduce the latter?

Inequality for sums of reciprocals

Exercice on periodic function

integral inequality with derivative

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