Question

Proof for integral absolute value inequality

score 68 · Answer 1 · 2023-11-14 20:23:11

68

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Proof for integral absolute value inequality

Published on 14 Nov 2023 - 20:23

score 65 · Answer 2 · 2023-11-21 22:35:16

65

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Doubt in some steps in the Nirenberg-Gagliardo-Sobolev inequality.

Published on 21 Nov 2023 - 22:35

score 108 · Answer 3 · 2026-03-25 11:01:01

108

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If all projections on the axis are integrable, do the iterated integrals exist?

Published on 25 Mar 2026 - 11:01

score 106 · Answer 4 · 2023-11-23 18:09:12

106

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Use the definition to find $\int_0^2f(x)dx$ where $f (x )=\cases{ 1,&$x \ne 1$\\2,& $x = 1$}$

Published on 23 Nov 2023 - 18:09

score 1k · Answer 5 · 2023-11-27 04:15:40

1k

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Why did the author write "Why?"? Any deep reason? ("Calculus Fourth Edition" by Michael Spivak)

Published on 27 Nov 2023 - 4:15

score 34 · Answer 6 · 2026-03-29 10:07:52

34

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Combination of function values on subinterval is bounded by $\inf$/$\sup$ of function.

Published on 29 Mar 2026 - 10:07

score 49 · Answer 7 · 2026-03-29 08:15:58

49

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Suppose that for each $a < b$ s.t $a, b \in [0, 1]$ there exists $t_1, t_2 \in [a, b]$ which satisfies $g(t_2) \leq f(t_1)$

Published on 29 Mar 2026 - 8:15

score 36 · Answer 8 · 2026-03-25 23:42:31

36

Views

For an arbitrary continuous curve $\gamma:[0,1]\to\mathbb R^n$, does the Riemann-Stieltjes integral $\int_0^1\gamma(t)\wedge d\gamma(t)$ exist?

Published on 25 Mar 2026 - 23:42

score 92 · Answer 9 · 2026-03-29 11:50:08

92

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prove that $\int_{a}^{c} f(x) \,dx = \int_{a}^{b} f(x) \,dx + \int_{b}^{c} f(x) \,dx $

Published on 29 Mar 2026 - 11:50

score 51 · Answer 10 · 2026-03-26 01:01:50

51

Views

Doubt about Rudin exercise 6.3 a

Published on 26 Mar 2026 - 1:01

score 116 · Answer 11 · 2023-12-11 17:10:12

116

Views

Attempt at proving the first part of the FTC

Published on 11 Dec 2023 - 17:10

score 63 · Answer 12 · 2023-12-12 00:54:57

63

Views

Convergence of Partial Sums

Published on 12 Dec 2023 - 0:54

score 93 · Answer 13 · 2026-03-25 22:09:24

93

Views

Integral of a piecewise continuous function - is this correct?

Published on 25 Mar 2026 - 22:09

score 33 · Answer 14 · 2023-12-14 17:47:21

33

Views

How to prove Thomae's function is continuous at all irrationals?

Published on 14 Dec 2023 - 17:47

score 77 · Answer 15 · 2026-03-28 07:38:33

77

Views

How bad is the error in the volume of a transformed region, when the transformation is approximated as linear?

Published on 28 Mar 2026 - 7:38

List Question

Proof for integral absolute value inequality

Doubt in some steps in the Nirenberg-Gagliardo-Sobolev inequality.

If all projections on the axis are integrable, do the iterated integrals exist?

Use the definition to find $\int_0^2f(x)dx$ where $f (x )=\cases{ 1,&$x \ne 1$\\2,& $x = 1$}$

Why did the author write "Why?"? Any deep reason? ("Calculus Fourth Edition" by Michael Spivak)

Combination of function values on subinterval is bounded by $\inf$/$\sup$ of function.

Suppose that for each $a < b$ s.t $a, b \in [0, 1]$ there exists $t_1, t_2 \in [a, b]$ which satisfies $g(t_2) \leq f(t_1)$

For an arbitrary continuous curve $\gamma:[0,1]\to\mathbb R^n$, does the Riemann-Stieltjes integral $\int_0^1\gamma(t)\wedge d\gamma(t)$ exist?

prove that $\int_{a}^{c} f(x) \,dx = \int_{a}^{b} f(x) \,dx + \int_{b}^{c} f(x) \,dx $

Doubt about Rudin exercise 6.3 a

Attempt at proving the first part of the FTC

Convergence of Partial Sums

Integral of a piecewise continuous function - is this correct?

How to prove Thomae's function is continuous at all irrationals?

How bad is the error in the volume of a transformed region, when the transformation is approximated as linear?

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