Question

Possible Pitfalls when Converting a Infinite Series to a Riemann Integral

score 36 · Answer 1 · 2026-04-02 00:31:19

36

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Possible Pitfalls when Converting a Infinite Series to a Riemann Integral

Published on 02 Apr 2026 - 0:31

score 48 · Answer 2 · 2026-03-26 14:42:02

48

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Is a real random variable's moment-generating function the Laplace-Stieltjes transform of its CDF?

Published on 26 Mar 2026 - 14:42

score 64 · Answer 3 · 2022-07-23 15:43:39

Justifying the need for homeomorphism $\psi$ to satisfy a Lipschitz condition to prove $f\circ\psi$ is Riemann integrable given f is.

score 443 · Answer 4 · 2026-03-26 14:43:02

443

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Let $\alpha$ be an increasing function on $[a,b]$. Show that $\int^a_b\alpha d \alpha = \frac{1}{2}[\alpha (b)^2 - \alpha(a)^2]$

Published on 26 Mar 2026 - 14:43

score 37 · Answer 5 · 2022-08-01 05:04:43

37

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Why does calculation of integral through Riemann and Lesbesgue concept match though the sets are different?

Published on 01 Aug 2022 - 5:04

score 419 · Answer 6 · 2026-02-27 09:29:34

419

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limit $\lim_{k \to \infty} \int_{0}^{1} \frac{kx^k}{1+x} dx$

Published on 27 Feb 2026 - 9:29

score 51 · Answer 7 · 2026-03-25 22:10:43

51

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Can you derive the limit definition of an integral with an Euler's method construction?

Published on 25 Mar 2026 - 22:10

score 69 · Answer 8 · 2022-08-05 16:57:45

69

Views

Evaluate $\int_1^e\frac{1}{x}dx$ using upper and lower sums

Published on 05 Aug 2022 - 16:57

score 133 · Answer 9 · 2026-03-30 01:31:10

133

Views

Asymptotic behavior of $ \int^\infty_{-\infty} \frac{x^2 \exp(-(x-a)^2)}{1+Aa^{-1}\exp(-x^2/(1+a^2))} dx$ as $a\to 0$

Published on 30 Mar 2026 - 1:31

score 81 · Answer 10 · 2022-08-13 21:49:29

81

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Does derivative of antiderivative always equal the integrand function?

Published on 13 Aug 2022 - 21:49

score 405 · Answer 11 · 2022-08-14 22:44:45

405

Views

Bounded function is Riemann-Integrable if and only if its upper and lower integrals are equal

Published on 14 Aug 2022 - 22:44

score 117 · Answer 12 · 2022-08-15 21:51:05

117

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Replacing $\inf/\sup$ by $\max/\min$ in the definition of the Riemann upper/lower sum

Published on 15 Aug 2022 - 21:51

score 106 · Answer 13 · 2022-08-17 11:39:22

106

Views

Doubt about counterexample of the Monotone convergence theorem and Riemann integral

Published on 17 Aug 2022 - 11:39

score 54 · Answer 14 · 2022-08-20 01:35:54

54

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$f\in\mathcal{R}[a,b]$ with $(\dot{\mathcal{P}}_n)\ni||\dot{\mathcal{P}_n}||\to 0.$. Show $\lim_{n\to\infty}S(f;\dot{\mathcal{P}_n})=\int_a^b f$.

Published on 20 Aug 2022 - 1:35

score 42 · Answer 15 · 2022-08-24 11:01:40

42

Views

Prove that this function is Riemann integrable using upper and lower sums

Published on 24 Aug 2022 - 11:01

List Question

Possible Pitfalls when Converting a Infinite Series to a Riemann Integral

Is a real random variable's moment-generating function the Laplace-Stieltjes transform of its CDF?

Justifying the need for homeomorphism $\psi$ to satisfy a Lipschitz condition to prove $f\circ\psi$ is Riemann integrable given f is.

Let $\alpha$ be an increasing function on $[a,b]$. Show that $\int^a_b\alpha d \alpha = \frac{1}{2}[\alpha (b)^2 - \alpha(a)^2]$

Why does calculation of integral through Riemann and Lesbesgue concept match though the sets are different?

limit $\lim_{k \to \infty} \int_{0}^{1} \frac{kx^k}{1+x} dx$

Can you derive the limit definition of an integral with an Euler's method construction?

Evaluate $\int_1^e\frac{1}{x}dx$ using upper and lower sums

Asymptotic behavior of $ \int^\infty_{-\infty} \frac{x^2 \exp(-(x-a)^2)}{1+Aa^{-1}\exp(-x^2/(1+a^2))} dx$ as $a\to 0$

Does derivative of antiderivative always equal the integrand function?

Bounded function is Riemann-Integrable if and only if its upper and lower integrals are equal

Replacing $\inf/\sup$ by $\max/\min$ in the definition of the Riemann upper/lower sum

Doubt about counterexample of the Monotone convergence theorem and Riemann integral

$f\in\mathcal{R}[a,b]$ with $(\dot{\mathcal{P}}_n)\ni||\dot{\mathcal{P}_n}||\to 0.$. Show $\lim_{n\to\infty}S(f;\dot{\mathcal{P}_n})=\int_a^b f$.

Prove that this function is Riemann integrable using upper and lower sums

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