List questions from riemann-integration

Published on 01 Mar 2019 - 23:13

809

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proof that there is $c \in [a,b]$ such that $f(c) = g(c)$

Published on 26 Mar 2026 - 3:00

83

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$\frac{1}{2^p}\sum_{k=1}^{2^p}f\biggl(\frac{k}{2^p}\biggl)=\int_0^1f(x)dx$ implies $f$ is constant

Published on 05 Mar 2019 - 11:40

371

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Integration and null function

Published on 07 Mar 2019 - 6:07

228

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$\int_a^b f(x)g(x)\ dx=g(a)\int_a^{x_0}f(x)\ dx+g(b)\int_{x_0}^bf(x)dx$

Published on 07 Mar 2019 - 10:25

148

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Evaluate using Riemann sums $\int_{\pi/2}^{3\pi/2}(4\sin 3x - 3 \cos 4x)dx$

Published on 07 Mar 2019 - 18:31

367

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Prove that a function is Riemann Integrable

Published on 08 Mar 2019 - 22:51

166

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Find the limit of $\lim\limits_{n\to\infty}\frac{1}{n^2}\sum\limits_{k=1}^{n}k\arctan{\big(\frac{pk-p+1}{pn}\big)}$

Published on 26 Mar 2026 - 2:57

298

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Example of sequence of continuous function which is not Riemann integrable with following property

Published on 10 Mar 2019 - 13:03

125

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Integration and existence of an antiderivative

Published on 10 Mar 2019 - 23:59

81

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Integration and a function increasing

Published on 11 Mar 2019 - 1:57

64

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limit of Integral of product of convergent functions

Published on 11 Mar 2019 - 9:52

30

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Existence of antiderivative of a function

Published on 11 Mar 2019 - 22:56

47

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Riemann-Stieltjes Integration-IVT

Published on 26 Mar 2026 - 9:40

433

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If $f$ is integrable, then $\| f\|$ is also integrable.

Published on 13 Mar 2019 - 22:05

List Question

Is Young's inequality true without the continuity assumption?

proof that there is $c \in [a,b]$ such that $f(c) = g(c)$

$\frac{1}{2^p}\sum_{k=1}^{2^p}f\biggl(\frac{k}{2^p}\biggl)=\int_0^1f(x)dx$ implies $f$ is constant

Integration and null function

$\int_a^b f(x)g(x)\ dx=g(a)\int_a^{x_0}f(x)\ dx+g(b)\int_{x_0}^bf(x)dx$

Evaluate using Riemann sums $\int_{\pi/2}^{3\pi/2}(4\sin 3x - 3 \cos 4x)dx$

Prove that a function is Riemann Integrable

Find the limit of $\lim\limits_{n\to\infty}\frac{1}{n^2}\sum\limits_{k=1}^{n}k\arctan{\big(\frac{pk-p+1}{pn}\big)}$

Example of sequence of continuous function which is not Riemann integrable with following property

Integration and existence of an antiderivative

Integration and a function increasing

limit of Integral of product of convergent functions

Existence of antiderivative of a function

Riemann-Stieltjes Integration-IVT

If $f$ is integrable, then $\| f\|$ is also integrable.

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