Question

Prove or disprove: $\lim_{a\to 1^-}E(a)=1$ for $E(a)$ elliptic integral of second kind

score 68 · Answer 1 · 2019-12-18 07:32:15

68

Views

Prove or disprove: $\lim_{a\to 1^-}E(a)=1$ for $E(a)$ elliptic integral of second kind

Published on 18 Dec 2019 - 7:32

score 539 · Answer 2 · 2019-12-20 17:28:29

539

Views

Integrability of the derivative of an increasing function- MIT primes 2020 A2

Published on 20 Dec 2019 - 17:28

score 184 · Answer 3 · 2026-03-27 07:40:03

184

Views

A formula for the difference between Riemann sum and Riemann integral

Published on 27 Mar 2026 - 7:40

score 52 · Answer 4 · 2019-12-22 14:23:01

52

Views

$\int_{3}^{x^2} e^{t^2} +1dt$ minima and inf

Published on 22 Dec 2019 - 14:23

score 1k · Answer 5 · 2026-02-24 00:47:24

1k

Views

Uniformly bounded sequence of Riemann integrable functions

Published on 24 Feb 2026 - 0:47

score 468 · Answer 6 · 2026-03-27 07:41:31

468

Views

Substitution theorem for definite integrals and indefinite integrals.

Published on 27 Mar 2026 - 7:41

score 257 · Answer 7 · 2019-12-23 23:58:56

257

Views

Proof of integrability

Published on 23 Dec 2019 - 23:58

score 87 · Answer 8 · 2019-12-26 17:29:44

87

Views

Riemann non-integrability on sub-interval $[c,d] \subset [a,b]$ implies Riemann non-integrability on interval $[a,b]$?

Published on 26 Dec 2019 - 17:29

score 81 · Answer 9 · 2019-12-26 21:11:46

81

Views

A bounded function which is Riemann integrable on any interval $[a+\epsilon, b]$, $\epsilon \in (0,b-a)$

Published on 26 Dec 2019 - 21:11

score 467 · Answer 10 · 2019-12-27 03:20:13

467

Views

Exercise 5.3.7 Introduction to Real Analysis by Jiri Lebl (Fundamental Theorem of Calculus)

Published on 27 Dec 2019 - 3:20

score 651 · Answer 11 · 2019-12-27 22:09:05

651

Views

Suppose $f$ has a discontinuity at $c \in (a,b)$, show that $F(x) = \int_a^x f$ is not differentiable at $c$

Published on 27 Dec 2019 - 22:09

score 154 · Answer 12 · 2019-12-28 19:35:34

154

Views

Bounding a Riemann Stieltjes integral.

Published on 28 Dec 2019 - 19:35

score 89 · Answer 13 · 2019-12-29 03:21:02

Suppose $f : [1, \infty) \to \mathbb{R}$ is such that $g(x) : = x^2f(x)$ is a bounded function. Prove that $\int_1^\infty f$ converges.

score 336 · Answer 14 · 2019-12-29 03:36:32

Find an example of an unbounded continuous function $f : [0, \infty) \to \mathbb{R}$ that is nonnegative and such that $\int_0^\infty f < \infty$.

score 92 · Answer 15 · 2019-12-29 13:49:55

92

Views

How to prove that a function is Riemann integrable?

Published on 29 Dec 2019 - 13:49

List Question

Prove or disprove: $\lim_{a\to 1^-}E(a)=1$ for $E(a)$ elliptic integral of second kind

Integrability of the derivative of an increasing function- MIT primes 2020 A2

A formula for the difference between Riemann sum and Riemann integral

$\int_{3}^{x^2} e^{t^2} +1dt$ minima and inf

Uniformly bounded sequence of Riemann integrable functions

Substitution theorem for definite integrals and indefinite integrals.

Proof of integrability

Riemann non-integrability on sub-interval $[c,d] \subset [a,b]$ implies Riemann non-integrability on interval $[a,b]$?

A bounded function which is Riemann integrable on any interval $[a+\epsilon, b]$, $\epsilon \in (0,b-a)$

Exercise 5.3.7 Introduction to Real Analysis by Jiri Lebl (Fundamental Theorem of Calculus)

Suppose $f$ has a discontinuity at $c \in (a,b)$, show that $F(x) = \int_a^x f$ is not differentiable at $c$

Bounding a Riemann Stieltjes integral.

Suppose $f : [1, \infty) \to \mathbb{R}$ is such that $g(x) : = x^2f(x)$ is a bounded function. Prove that $\int_1^\infty f$ converges.

Find an example of an unbounded continuous function $f : [0, \infty) \to \mathbb{R}$ that is nonnegative and such that $\int_0^\infty f < \infty$.

How to prove that a function is Riemann integrable?

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