Question

Proof that $\forall a<b, f(x)=x$ is Riemann integrable on the interval $[a,b]$ and $\int_a^{b} f dx = \frac{1}{2} (b^2 - a^2)$

score 87 · Answer 1 · 2016-12-21 03:50:03

87

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Proof that $\forall a<b, f(x)=x$ is Riemann integrable on the interval $[a,b]$ and $\int_a^{b} f dx = \frac{1}{2} (b^2 - a^2)$

Published on 21 Dec 2016 - 3:50

score 741 · Answer 2 · 2026-03-29 10:12:14

741

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Thomae's function $2$ dimensional is integrable

Published on 29 Mar 2026 - 10:12

score 474 · Answer 3 · 2016-12-26 08:13:07

474

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Finding out the limit: $\lim_{n \to \infty}\frac{1}{n}\sum_{k=0}^{n}\sqrt {k(n-k)}$

Published on 26 Dec 2016 - 8:13

score 453 · Answer 4 · 2016-12-26 20:24:08

453

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Prove that $f\circ g$ is Riemann integrable on $[a,b]$

Published on 26 Dec 2016 - 20:24

score 671 · Answer 5 · 2016-12-27 22:54:39

671

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Prove that there exists a continuous function $g$ such that $\int_a^b|f-g| \lt \epsilon$

Published on 27 Dec 2016 - 22:54

score 59 · Answer 6 · 2016-12-28 15:23:50

59

Views

Prove $\sum_{i=1}^{n}i^r = \frac{n^{r+1}}{r+1}+\frac{n^r}{2}+P_r(n)$ Such that $P_r$ is a polynomial with degree less than $r$

Published on 28 Dec 2016 - 15:23

score 72 · Answer 7 · 2016-12-28 19:41:52

72

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Is the series $\sum\limits_{k=1}^{\infty}( a^{\frac{1}{k}}-1)$ convergent?

Published on 28 Dec 2016 - 19:41

score 1.2k · Answer 8 · 2017-01-01 13:32:25

1.2k

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Prove an Riemann integrable function which equals to zero except on a null set implies its integral is zero

Published on 01 Jan 2017 - 13:32

score 295 · Answer 9 · 2017-01-03 12:28:29

295

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Extended integral

Published on 03 Jan 2017 - 12:28

score 35 · Answer 10 · 2017-01-04 12:29:49

35

Views

Doubt on properties of Lebesgue and Riemann integrals

Published on 04 Jan 2017 - 12:29

score 947 · Answer 11 · 2017-01-04 13:32:49

947

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A non-Riemann-integrable function $f\colon [0, 1]^2 \to \mathbb{R}$ such that $f(\cdot, y), f(x, \cdot)$ are Riemann integrable.

Published on 04 Jan 2017 - 13:32

score 81 · Answer 12 · 2017-01-04 19:37:26

81

Views

On the foundations of abstract Riemannian integration

Published on 04 Jan 2017 - 19:37

score 903 · Answer 13 · 2017-01-04 22:58:26

903

Views

A different proof for "If $f$ is Riemann integrable, Then so is $f^2$ "

Published on 04 Jan 2017 - 22:58

score 1.2k · Answer 14 · 2017-01-06 17:49:00

1.2k

Views

Why was it necessary for the Riemann integral to consider all partitions and taggings?

Published on 06 Jan 2017 - 17:49

score 567 · Answer 15 · 2017-01-06 20:27:29

567

Views

Proving Lebesgue Integration Yields Same Answer As Riemann

Published on 06 Jan 2017 - 20:27

List Question

Proof that $\forall a<b, f(x)=x$ is Riemann integrable on the interval $[a,b]$ and $\int_a^{b} f dx = \frac{1}{2} (b^2 - a^2)$

Thomae's function $2$ dimensional is integrable

Finding out the limit: $\lim_{n \to \infty}\frac{1}{n}\sum_{k=0}^{n}\sqrt {k(n-k)}$

Prove that $f\circ g$ is Riemann integrable on $[a,b]$

Prove that there exists a continuous function $g$ such that $\int_a^b|f-g| \lt \epsilon$

Prove $\sum_{i=1}^{n}i^r = \frac{n^{r+1}}{r+1}+\frac{n^r}{2}+P_r(n)$ Such that $P_r$ is a polynomial with degree less than $r$

Is the series $\sum\limits_{k=1}^{\infty}( a^{\frac{1}{k}}-1)$ convergent?

Prove an Riemann integrable function which equals to zero except on a null set implies its integral is zero

Extended integral

Doubt on properties of Lebesgue and Riemann integrals

A non-Riemann-integrable function $f\colon [0, 1]^2 \to \mathbb{R}$ such that $f(\cdot, y), f(x, \cdot)$ are Riemann integrable.

On the foundations of abstract Riemannian integration

A different proof for "If $f$ is Riemann integrable, Then so is $f^2$ "

Why was it necessary for the Riemann integral to consider all partitions and taggings?

Proving Lebesgue Integration Yields Same Answer As Riemann

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