Question

Integral of $f(x)=\begin{cases} \sin(x), & \text{if } \cos(x)\in \mathbb{Q}\\\sin^2(x), & \text{if }\cos(x) \notin \mathbb{Q} \end{cases}$

score 530 · Answer 1 · 2026-04-16 08:37:23

530

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Integral of $f(x)=\begin{cases} \sin(x), & \text{if } \cos(x)\in \mathbb{Q}\\\sin^2(x), & \text{if }\cos(x) \notin \mathbb{Q} \end{cases}$

Published on 16 Apr 2026 - 8:37

score 49 · Answer 2 · 2026-04-14 05:06:04

49

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score 68 · Answer 3 · 2026-04-11 11:12:33

68

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score 468 · Answer 4 · 2026-04-10 08:30:50

468

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score 54 · Answer 5 · 2026-04-16 06:15:53

54

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1k

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score 1.5k · Answer 7 · 2026-04-23 04:48:08

1.5k

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score 184 · Answer 8 · 2026-04-01 00:52:51

184

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score 84 · Answer 9 · 2026-04-06 17:00:37

84

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1.6k

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score 53 · Answer 11 · 2026-04-20 12:21:10

53

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score 1.2k · Answer 12 · 2026-04-19 18:33:46

1.2k

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score 3.7k · Answer 13 · 2026-04-23 20:02:12

3.7k

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score 989 · Answer 14 · 2026-04-07 06:46:06

989

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score 11.1k · Answer 15 · 2026-04-21 10:19:25

11.1k

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Published on 21 Apr 2026 - 10:19

List Question

Integral of $f(x)=\begin{cases} \sin(x), & \text{if } \cos(x)\in \mathbb{Q}\\\sin^2(x), & \text{if }\cos(x) \notin \mathbb{Q} \end{cases}$

Dose convergence in measure imply convergence almost every where?

Lebesgue integral/measure issue

No "Conditional Convergence" in Lebesgue Integration

Uniform Limit vs. Integral Mean

Integrable absolutely continuous $f$ with integrable $f'$ has limit $0$ at infinity

Expected value & Lebesgue integral

Set of discontinuities of bounded function has measure 0.

How bad can be the behavior of Lebesgue integrable functions?

Lebesgue integral - interpretation

Interpretation of $ \int_A f \ d\mu $ in case $\mu (A) = \infty$

Interchanging Lebesgue integrals with limits when the limits of integration are variable

Are upper and lower Lebesgue integrals equal for every $f$?

Is an a.e finite function integrable?

The Lebesgue integral of an integrable function is continuous

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