Question

Why is it that $\sum_{n=1}^\infty \frac{1}{n^2}=\frac{\pi^2}{6}$ is not less than $\int_1^\infty \frac{dx}{x^2} = 1$?

score 980 · Answer 1 · 2026-03-26 11:01:18

980

Views

Why is it that $\sum_{n=1}^\infty \frac{1}{n^2}=\frac{\pi^2}{6}$ is not less than $\int_1^\infty \frac{dx}{x^2} = 1$?

Published on 26 Mar 2026 - 11:01

score 40 · Answer 2 · 2018-02-27 07:58:05

40

Views

Definite integral on a bivariate normal

Published on 27 Feb 2018 - 7:58

score 54 · Answer 3 · 2018-02-27 08:13:04

54

Views

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a continuous, diffrentiable given function. Find $\int^b_af^{(3)}(x)\ f'(x)dx$

Published on 27 Feb 2018 - 8:13

score 87 · Answer 4 · 2026-04-09 03:38:08

87

Views

What is the equality of this integral which includes Dirac-Delta function?

Published on 09 Apr 2026 - 3:38

score 40 · Answer 5 · 2018-02-27 13:09:37

40

Views

prove the validity of unit step function

Published on 27 Feb 2018 - 13:09

score 33.7k · Answer 6 · 2026-04-01 17:11:17

33.7k

Views

Area enclosed between 3 curves

Published on 01 Apr 2026 - 17:11

score 1k · Answer 7 · 2026-04-09 18:01:29

1k

Views

Understanding the difference between $\Delta x$ and $dx$

Published on 09 Apr 2026 - 18:01

score 54 · Answer 8 · 2018-02-27 21:03:52

54

Views

Let $1\lt k \in\mathbb{N}. $ Prove: $\frac{1}{2}+\frac{1}{3}+...+\frac{1}{k}\lt ln(k) \lt 1+ \frac{1}{2}+...+\frac{1}{k-1}$ using integration.

Published on 27 Feb 2018 - 21:03

score 60 · Answer 9 · 2026-03-25 11:16:29

60

Views

limit as $\delta \rightarrow 0 \int_{a + \delta}^{b} f(x)dx = \int_{a}^{b}f(x)dx$?

Published on 25 Mar 2026 - 11:16

score 58 · Answer 10 · 2026-04-08 19:35:44

58

Views

Finding the derivative of an integral function

Published on 08 Apr 2026 - 19:35

score 100 · Answer 11 · 2018-02-28 02:36:18

100

Views

A confusing mistake in evaluating $\int_{-\infty}^{\infty}{\frac{e^{-x^2}}{x^2+a^2}dx}$

Published on 28 Feb 2018 - 2:36

score 185 · Answer 12 · 2026-04-03 11:39:35

185

Views

Maximum of a definite integral

Published on 03 Apr 2026 - 11:39

score 94 · Answer 13 · 2026-03-26 10:46:14

94

Views

Prove an inequality for the cosine integral

Published on 26 Mar 2026 - 10:46

score 103 · Answer 14 · 2018-02-28 15:51:19

103

Views

Reduction to triple integral

Published on 28 Feb 2018 - 15:51

score 93 · Answer 15 · 2018-02-28 16:22:10

93

Views

Calculate the double limit $\lim_{n\to\infty}(\lim_{k\to\infty}\int_{0}^{1}\left ( \frac{[kx]}{k} \right )^{n}dx))$

Published on 28 Feb 2018 - 16:22

List Question

Why is it that $\sum_{n=1}^\infty \frac{1}{n^2}=\frac{\pi^2}{6}$ is not less than $\int_1^\infty \frac{dx}{x^2} = 1$?

Definite integral on a bivariate normal

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a continuous, diffrentiable given function. Find $\int^b_af^{(3)}(x)\ f'(x)dx$

What is the equality of this integral which includes Dirac-Delta function?

prove the validity of unit step function

Area enclosed between 3 curves

Understanding the difference between $\Delta x$ and $dx$

Let $1\lt k \in\mathbb{N}. $ Prove: $\frac{1}{2}+\frac{1}{3}+...+\frac{1}{k}\lt ln(k) \lt 1+ \frac{1}{2}+...+\frac{1}{k-1}$ using integration.

limit as $\delta \rightarrow 0 \int_{a + \delta}^{b} f(x)dx = \int_{a}^{b}f(x)dx$?

Finding the derivative of an integral function

A confusing mistake in evaluating $\int_{-\infty}^{\infty}{\frac{e^{-x^2}}{x^2+a^2}dx}$

Maximum of a definite integral

Prove an inequality for the cosine integral

Reduction to triple integral

Calculate the double limit $\lim_{n\to\infty}(\lim_{k\to\infty}\int_{0}^{1}\left ( \frac{[kx]}{k} \right )^{n}dx))$

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