Question

Help with this integral: $\int_{0}^{1}\frac{1}{1+x^{2}}dx$ (Riemann)

score 183 · Answer 1 · 2017-06-05 23:30:17

183

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Help with this integral: $\int_{0}^{1}\frac{1}{1+x^{2}}dx$ (Riemann)

Published on 05 Jun 2017 - 23:30

score 39 · Answer 2 · 2017-06-06 19:27:39

39

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Is it true, that $\lim_{x \to \infty} {\bigg(\frac {\int_a^b{g^{x}(t)dt}}{b - a}\bigg)}^{\frac {1}{x}} = max(g(t))$?

Published on 06 Jun 2017 - 19:27

score 189 · Answer 3 · 2017-06-07 21:47:22

189

Views

Proving that if $f$ is Riemann-integrable on $[a, b]$, then cardinality of set of points of continuity on $[a, b]$ is equal to $\mathbb{R}$

Published on 07 Jun 2017 - 21:47

score 285 · Answer 4 · 2017-06-09 16:53:07

285

Views

Prove that the function $f$ is identically zero by the given condition.

Published on 09 Jun 2017 - 16:53

score 52 · Answer 5 · 2017-06-11 08:13:56

52

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Do we get a more general integral if we allow countable sums in the Riemann integral?

Published on 11 Jun 2017 - 8:13

score 137 · Answer 6 · 2017-06-12 01:20:29

137

Views

Visualizing the Riemann-Stieltjes integral

Published on 12 Jun 2017 - 1:20

score 2.7k · Answer 7 · 2017-06-12 14:06:58

2.7k

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Theorem 6.10 in Baby Rudin: If $f$ is bounded on $[a, b]$ with only finitely many points of discontinuity at which $\alpha$ is continuous, then

Published on 12 Jun 2017 - 14:06

score 54 · Answer 8 · 2017-06-14 10:48:58

54

Views

How to find out the riemann integral of following function?

Published on 14 Jun 2017 - 10:48

score 45 · Answer 9 · 2017-06-16 08:36:48

45

Views

$f:[0,1] \to \mathbb R$ be a function such that $f(x)=x^2 , \forall x \in \mathbb Q ; f(x)=x^3$ ; what is the upper and lower integral of $f$?

Published on 16 Jun 2017 - 8:36

score 52 · Answer 10 · 2017-06-16 19:03:02

52

Views

Continunuity of the generalized primitive

Published on 16 Jun 2017 - 19:03

score 210 · Answer 11 · 2017-06-17 10:10:27

210

Views

show that this function is not Riemann integrable on $[0,1].$

Published on 17 Jun 2017 - 10:10

score 51 · Answer 12 · 2017-06-17 14:23:04

51

Views

Riemann integrability of a given function

Published on 17 Jun 2017 - 14:23

score 440 · Answer 13 · 2026-03-31 05:34:44

440

Views

Is $f$ Riemann integrable?

Published on 31 Mar 2026 - 5:34

score 61 · Answer 14 · 2026-03-31 05:31:49

61

Views

A question regarding calculating a limit

Published on 31 Mar 2026 - 5:31

score 48 · Answer 15 · 2017-06-19 17:39:35

48

Views

Show or contradict that $f$ is Rieman integrable.

Published on 19 Jun 2017 - 17:39

List Question

Help with this integral: $\int_{0}^{1}\frac{1}{1+x^{2}}dx$ (Riemann)

Is it true, that $\lim_{x \to \infty} {\bigg(\frac {\int_a^b{g^{x}(t)dt}}{b - a}\bigg)}^{\frac {1}{x}} = max(g(t))$?

Proving that if $f$ is Riemann-integrable on $[a, b]$, then cardinality of set of points of continuity on $[a, b]$ is equal to $\mathbb{R}$

Prove that the function $f$ is identically zero by the given condition.

Do we get a more general integral if we allow countable sums in the Riemann integral?

Visualizing the Riemann-Stieltjes integral

Theorem 6.10 in Baby Rudin: If $f$ is bounded on $[a, b]$ with only finitely many points of discontinuity at which $\alpha$ is continuous, then

How to find out the riemann integral of following function?

$f:[0,1] \to \mathbb R$ be a function such that $f(x)=x^2 , \forall x \in \mathbb Q ; f(x)=x^3$ ; what is the upper and lower integral of $f$?

Continunuity of the generalized primitive

show that this function is not Riemann integrable on $[0,1].$

Riemann integrability of a given function

Is $f$ Riemann integrable?

A question regarding calculating a limit

Show or contradict that $f$ is Rieman integrable.

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