List questions from riemann-integration

Published on 22 Mar 2026 - 12:59

137

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Prove $\int_a^b f(x)dx=(b-a)f\{a+\theta(b-a)\}$ for some $\theta\in(0,1)$.

Published on 11 Mar 2018 - 15:22

56

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Find $\sup\{f(x)|x\in [\frac{r-1}{n}, \frac{r}{n}]\cap Q^c\}$

Published on 13 Mar 2018 - 5:04

210

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Riemann Integration of Parabola

Published on 15 Mar 2018 - 4:11

220

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Riemann integral of discrete white noise

Published on 23 Mar 2026 - 1:26

2.3k

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Proof explanation of linearity property of Riemann integrable functions

Published on 16 Mar 2018 - 11:45

171

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How to represent $ \int_0^t B_s \, dB_s$ as the limit of a discrete sum?

Published on 25 Mar 2026 - 1:18

529

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Convolution and Riemann sum

Published on 25 Mar 2026 - 7:40

49

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Let $f:[a,b]\to \mathbb{R}$ is integrable on $[a,b]$. Show that $f_1:[a,b]\to \mathbb{R}$ such that $f_1(x)=\sup\{f(x), 0\}$, is integrable.

Published on 19 Mar 2018 - 6:27

179

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Chacking integrability of a piecewise function

Published on 19 Mar 2018 - 7:07

103

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Show that $\frac{1}{3}<\int_0^1\frac{1}{1+x+x^2} \, dx <\frac{\pi}{4}$

Published on 19 Mar 2018 - 16:48

114

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Find $\lim_{n \to \infty}\sum_{k=1}^n \frac{(-1)^{k+1}}{2k+1}$

Published on 21 Mar 2018 - 16:26

286

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Riemann Integrability and the Fundamental Theorem of Calculus

Published on 22 Mar 2018 - 14:16

334

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Proof that $f$ is Riemann integrable without Lebesgue criteria

Published on 25 Mar 2026 - 9:49

33

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If F(x)=$\int_0^xf(x)dx$ for $x\in[0,3]$, find $F$.

Published on 26 Mar 2018 - 4:52

List Question

Is it integration or not

Prove $\int_a^b f(x)dx=(b-a)f\{a+\theta(b-a)\}$ for some $\theta\in(0,1)$.

Find $\sup\{f(x)|x\in [\frac{r-1}{n}, \frac{r}{n}]\cap Q^c\}$

Riemann Integration of Parabola

Riemann integral of discrete white noise

Proof explanation of linearity property of Riemann integrable functions

How to represent $ \int_0^t B_s \, dB_s$ as the limit of a discrete sum?

Convolution and Riemann sum

Let $f:[a,b]\to \mathbb{R}$ is integrable on $[a,b]$. Show that $f_1:[a,b]\to \mathbb{R}$ such that $f_1(x)=\sup\{f(x), 0\}$, is integrable.

Chacking integrability of a piecewise function

Show that $\frac{1}{3}<\int_0^1\frac{1}{1+x+x^2} \, dx <\frac{\pi}{4}$

Find $\lim_{n \to \infty}\sum_{k=1}^n \frac{(-1)^{k+1}}{2k+1}$

Riemann Integrability and the Fundamental Theorem of Calculus

Proof that $f$ is Riemann integrable without Lebesgue criteria

If F(x)=$\int_0^xf(x)dx$ for $x\in[0,3]$, find $F$.

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