Question

Show that $\int_{0}^{\pi/6} {\cos (x^2)}\mathrm{d}x\ge\frac12$.

score 517 · Answer 1 · 2026-04-15 09:05:04

517

Views

Show that $\int_{0}^{\pi/6} {\cos (x^2)}\mathrm{d}x\ge\frac12$.

Published on 15 Apr 2026 - 9:05

score 113 · Answer 2 · 2026-04-16 01:34:03

113

Views

Compute the limit $\lim_{n\to\infty} I_n(a)$ where $ I_n(a) :=\int_0^a \frac{x^n}{x^n+1}\,\mathrm{d}x, n\in N$.

Published on 16 Apr 2026 - 1:34

score 80 · Answer 3 · 2026-04-13 17:15:51

80

Views

Inequality used in proof of existence of SDE solutions?

Published on 13 Apr 2026 - 17:15

score 316 · Answer 4 · 2026-04-12 18:50:09

316

Views

Integration inequality, why can we pull e^t out of the integral and leave its e?

Published on 12 Apr 2026 - 18:50

score 2k · Answer 5 · 2026-04-09 21:37:02

2k

Views

Application of Gronwall Inequality to existence of solutions

Published on 09 Apr 2026 - 21:37

score 41 · Answer 6 · 2026-05-10 15:22:40

41

Views

Finding discrete solutions to inequality involving Exponential Integral

Published on 10 May 2026 - 15:22

score 344 · Answer 7 · 2026-04-16 05:45:57

344

Views

Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.

Published on 16 Apr 2026 - 5:45

score 64 · Answer 8 · 2026-04-15 15:17:33

64

Views

Help bounding a "norm"

Published on 15 Apr 2026 - 15:17

score 108 · Answer 9 · 2026-04-14 05:44:18

108

Views

Linear version of Gronwall's inequality, proof

Published on 14 Apr 2026 - 5:44

score 139 · Answer 10 · 2026-04-12 03:22:09

139

Views

Is it a well-known inequality?

Published on 12 Apr 2026 - 3:22

score 88 · Answer 11 · 2026-04-15 14:27:08

88

Views

How is the inequality of these integrals true?

Published on 15 Apr 2026 - 14:27

score 38 · Answer 12 · 2026-04-11 03:49:42

38

Views

prove inequality with an integral over region with unit length

Published on 11 Apr 2026 - 3:49

score 82 · Answer 13 · 2026-04-17 04:08:47

82

Views

$\int_0^1f(x)\cdot x^{n+1}\text{d}x > \int_0^1f(x)\cdot x^n\text{d}x \cdot \int_0^1f(x)\cdot x\text{d}x$

Published on 17 Apr 2026 - 4:08

score 103 · Answer 14 · 2026-04-16 22:43:30

103

Views

Prove that:$\int_{a}^{b}(2x^{3}-3(a+b)x^{2}+6abx)f'(x)dx\geq (a-b)^{3}f(a)$.

Published on 16 Apr 2026 - 22:43

score 74 · Answer 15 · 2026-04-13 21:48:47

74

Views

Given a sequence of Lp functions, does the integral commute with the lp norm?

Published on 13 Apr 2026 - 21:48

List Question

Show that $\int_{0}^{\pi/6} {\cos (x^2)}\mathrm{d}x\ge\frac12$.

Compute the limit $\lim_{n\to\infty} I_n(a)$ where $ I_n(a) :=\int_0^a \frac{x^n}{x^n+1}\,\mathrm{d}x, n\in N$.

Inequality used in proof of existence of SDE solutions?

Integration inequality, why can we pull e^t out of the integral and leave its e?

Application of Gronwall Inequality to existence of solutions

Finding discrete solutions to inequality involving Exponential Integral

Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.

Help bounding a "norm"

Linear version of Gronwall's inequality, proof

Is it a well-known inequality?

How is the inequality of these integrals true?

prove inequality with an integral over region with unit length

$\int_0^1f(x)\cdot x^{n+1}\text{d}x > \int_0^1f(x)\cdot x^n\text{d}x \cdot \int_0^1f(x)\cdot x\text{d}x$

Prove that:$\int_{a}^{b}(2x^{3}-3(a+b)x^{2}+6abx)f'(x)dx\geq (a-b)^{3}f(a)$.

Given a sequence of Lp functions, does the integral commute with the lp norm?

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