Question

Checking for the integrability of $\int_U \ln{\sqrt{x^2+y^2}}$ using exhaustions

score 41 · Answer 1 · 2022-04-19 21:35:38

41

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Checking for the integrability of $\int_U \ln{\sqrt{x^2+y^2}}$ using exhaustions

Published on 19 Apr 2022 - 21:35

score 328 · Answer 2 · 2022-04-21 19:44:26

328

Views

Why is the upper sum of a refinement less than the upper sum of the original partition.

Published on 21 Apr 2022 - 19:44

score 24 · Answer 3 · 2022-04-21 20:05:28

Example for $\int_a^b f(x)g(x)dx\neq g(a)\int_a^c f(x)dx + g(b) \int_c^b f(x)dx$ for $f\geq 0$ and g a non-monotonic function.

score 74 · Answer 4 · 2022-04-23 16:41:17

74

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A nice Romanian Olympiad integral (Proof Verification)

Published on 23 Apr 2022 - 16:41

score 553 · Answer 5 · 2026-04-05 14:29:17

553

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Category of partitions of an interval

Published on 05 Apr 2026 - 14:29

score 263 · Answer 6 · 2022-04-26 12:48:44

263

Views

Lebesgue criterion for Riemann integrability.

Published on 26 Apr 2022 - 12:48

score 33 · Answer 7 · 2022-04-26 13:09:14

33

Views

Prove that $\sup_x |\rho(x)-\rho_{\alpha}(x)| \leq |\rho'|_{L^{\infty}(\mathbb{R})} |1_{x>0}-h_{\alpha}|_{L^1}$

Published on 26 Apr 2022 - 13:09

score 94 · Answer 8 · 2026-04-01 22:39:04

94

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$\int_{-2}^xf(t)dt$ for $f(t) = \tiny\begin{cases} -1 \, &t<0 \\ 1 \, &t\ge 0 \end{cases} $, and its limit at $x=0$

Published on 01 Apr 2026 - 22:39

score 701 · Answer 9 · 2026-04-01 22:36:24

701

Views

Find integral of $\sqrt{x}$ using Riemann sum definition

Published on 01 Apr 2026 - 22:36

score 118 · Answer 10 · 2022-05-01 18:51:12

118

Views

Finding the volume of an $n$-dimensional simplex (recursion)

Published on 01 May 2022 - 18:51

score 38 · Answer 11 · 2022-05-02 00:41:11

38

Views

Supremum with respect to an object

Published on 02 May 2022 - 0:41

score 45 · Answer 12 · 2022-05-02 12:04:49

45

Views

proving the integral convention $\int_{a}^{b}f(x)dx = \int_{a}^{c}f(x)dx + \int_{c}^{b}f(x)dx$ using the epsilon-delta definition

Published on 02 May 2022 - 12:04

score 23 · Answer 13 · 2022-05-03 08:10:50

23

Views

Integration similar to consequences of Riemann lebesgue lemma

Published on 03 May 2022 - 8:10

score 435 · Answer 14 · 2022-05-03 15:56:57

435

Views

Composition of Riemann-integrable and increasing functions.

Published on 03 May 2022 - 15:56

score 50 · Answer 15 · 2026-02-24 02:46:21

50

Views

The limits of a definite integral using Mean Value theorem

Published on 24 Feb 2026 - 2:46

List Question

Checking for the integrability of $\int_U \ln{\sqrt{x^2+y^2}}$ using exhaustions

Why is the upper sum of a refinement less than the upper sum of the original partition.

Example for $\int_a^b f(x)g(x)dx\neq g(a)\int_a^c f(x)dx + g(b) \int_c^b f(x)dx$ for $f\geq 0$ and g a non-monotonic function.

A nice Romanian Olympiad integral (Proof Verification)

Category of partitions of an interval

Lebesgue criterion for Riemann integrability.

Prove that $\sup_x |\rho(x)-\rho_{\alpha}(x)| \leq |\rho'|_{L^{\infty}(\mathbb{R})} |1_{x>0}-h_{\alpha}|_{L^1}$

$\int_{-2}^xf(t)dt$ for $f(t) = \tiny\begin{cases} -1 \, &t<0 \\ 1 \, &t\ge 0 \end{cases} $, and its limit at $x=0$

Find integral of $\sqrt{x}$ using Riemann sum definition

Finding the volume of an $n$-dimensional simplex (recursion)

Supremum with respect to an object

proving the integral convention $\int_{a}^{b}f(x)dx = \int_{a}^{c}f(x)dx + \int_{c}^{b}f(x)dx$ using the epsilon-delta definition

Integration similar to consequences of Riemann lebesgue lemma

Composition of Riemann-integrable and increasing functions.

The limits of a definite integral using Mean Value theorem

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