Question

Integral Modulus Inequality

score 152 · Answer 1 · 2026-04-13 04:06:57

152

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Integral Modulus Inequality

Published on 13 Apr 2026 - 4:06

score 158 · Answer 2 · 2026-04-11 14:36:50

158

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Integral inequality (possible line integral)

Published on 11 Apr 2026 - 14:36

score 378 · Answer 3 · 2026-04-17 05:23:55

378

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Prove: $\overline{\int_{a}^{b}} (g+f)(x) \ dx = \int\limits_a^b {{f(x)}dx}+ \overline{\int_{a}^{b}} g(x) \ dx$

Published on 17 Apr 2026 - 5:23

score 117 · Answer 4 · 2026-04-16 09:10:07

117

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Finding $\min \frac{\left[\int_{0}^{1}f(x)\mathrm dx\right]^2}{\int_{0}^{1}(f(x))^3\mathrm dx}$ given that $f(0)=0$ and $0\lt f'(x)\le 1$

Published on 16 Apr 2026 - 9:10

score 38 · Answer 5 · 2026-04-17 05:01:27

38

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How to prove the inequality $\iint_{x^2+y^2 \leq 1} e^{x^2+y^2}dxdy \leq (\int_{\sqrt{\pi}/2}^{\sqrt{\pi}/2} e^{x^2}dx)^2$

Published on 17 Apr 2026 - 5:01

score 92 · Answer 6 · 2026-04-16 04:05:48

92

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Lower bound via Sobolev Inequality

Published on 16 Apr 2026 - 4:05

score 46 · Answer 7 · 2026-04-16 13:39:35

46

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Lower bound for integral $\int_0^\infty (1+2ax)^{-3/2}(1+2bx)^{-n/2} dx$ when $a+nb=1$

Published on 16 Apr 2026 - 13:39

score 67 · Answer 8 · 2026-04-16 14:30:41

67

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Inequality involving the definite integrals of cos(x) f(x) and sin(x) f(x)

Published on 16 Apr 2026 - 14:30

score 142 · Answer 9 · 2026-04-15 21:05:22

142

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Inequality involving the definite integrals of $\cos(x) f(x)$ and $\sin(x) f(x)$

Published on 15 Apr 2026 - 21:05

score 98 · Answer 10 · 2026-04-16 18:28:43

98

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Inequality for $\int_Ω (F(f_1(x))-F(f_2(x)))(f_1(x)-f_2(x))\,\mathrm dx$ for an increasing function $F$

Published on 16 Apr 2026 - 18:28

score 82 · Answer 11 · 2026-04-14 14:58:05

82

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Hardy’s inequality. Exercise 3.14 from Rudin’s RACA.

Published on 14 Apr 2026 - 14:58

score 53 · Answer 12 · 2026-04-17 12:16:05

53

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Does $f'>0$ and $f''\ge\alpha f^p$ on $[t_0/2,t_0]$ imply $f'(x)>\sqrt{\frac\alpha{p+1}}\sqrt{f^{p+1}(x)-f^{p+1}\left(\frac{t_0}2\right)}$?

Published on 17 Apr 2026 - 12:16

score 49 · Answer 13 · 2026-04-14 17:05:24

49

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Boundedness of the minimizing sequence for Korn's inequality

Published on 14 Apr 2026 - 17:05

score 179 · Answer 14 · 2026-04-13 02:42:18

179

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Gronwall inequality for integrable functions

Published on 13 Apr 2026 - 2:42

score 207 · Answer 15 · 2026-04-14 21:32:15

207

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Bounding an integral by splitting the interval of integration

Published on 14 Apr 2026 - 21:32

List Question

Integral Modulus Inequality

Integral inequality (possible line integral)

Prove: $\overline{\int_{a}^{b}} (g+f)(x) \ dx = \int\limits_a^b {{f(x)}dx}+ \overline{\int_{a}^{b}} g(x) \ dx$

Finding $\min \frac{\left[\int_{0}^{1}f(x)\mathrm dx\right]^2}{\int_{0}^{1}(f(x))^3\mathrm dx}$ given that $f(0)=0$ and $0\lt f'(x)\le 1$

How to prove the inequality $\iint_{x^2+y^2 \leq 1} e^{x^2+y^2}dxdy \leq (\int_{\sqrt{\pi}/2}^{\sqrt{\pi}/2} e^{x^2}dx)^2$

Lower bound via Sobolev Inequality

Lower bound for integral $\int_0^\infty (1+2ax)^{-3/2}(1+2bx)^{-n/2} dx$ when $a+nb=1$

Inequality involving the definite integrals of cos(x) f(x) and sin(x) f(x)

Inequality involving the definite integrals of $\cos(x) f(x)$ and $\sin(x) f(x)$

Inequality for $\int_Ω (F(f_1(x))-F(f_2(x)))(f_1(x)-f_2(x))\,\mathrm dx$ for an increasing function $F$

Hardy’s inequality. Exercise 3.14 from Rudin’s RACA.

Does $f'>0$ and $f''\ge\alpha f^p$ on $[t_0/2,t_0]$ imply $f'(x)>\sqrt{\frac\alpha{p+1}}\sqrt{f^{p+1}(x)-f^{p+1}\left(\frac{t_0}2\right)}$?

Boundedness of the minimizing sequence for Korn's inequality

Gronwall inequality for integrable functions

Bounding an integral by splitting the interval of integration

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