Question

Continuity of the improper integral $\int_{0}^{x}y^{-1/2}dy.$

score 146 · Answer 1 · 2026-04-16 04:52:07

146

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Continuity of the improper integral $\int_{0}^{x}y^{-1/2}dy.$

Published on 16 Apr 2026 - 4:52

score 216 · Answer 2 · 2026-04-14 01:29:45

216

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Value of the integral $\int_{a}^{a}f(x)dx?$

Published on 14 Apr 2026 - 1:29

score 196 · Answer 3 · 2026-04-16 23:14:59

196

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Convergence of an improper integral $I=\int_{0}^\infty x^a \ln{(1+\frac{1}{x^2})} dx$

Published on 16 Apr 2026 - 23:14

score 670 · Answer 4 · 2026-04-16 11:40:59

670

Views

Evaluating $\int_{0}^{\infty}{\sin(x)\sin(2x)\sin(3x)\ldots \sin(nx)\sin(n^{2}x) \over x^{n + 1}}\,dx $

Published on 16 Apr 2026 - 11:40

score 7k · Answer 5 · 2026-04-16 18:53:19

7k

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Evaluate$\int_0^1 \frac{x^{m-1} + x^{n-1}}{(1+x)^{m+n}}dx$ in terms of Beta function

Published on 16 Apr 2026 - 18:53

score 1.4k · Answer 6 · 2026-04-17 21:19:49

1.4k

Views

Convergence of an improper integral $I=\int_0^\infty \frac{\sin{x}-x\cos{x}}{x^\alpha}dx$

Published on 17 Apr 2026 - 21:19

score 1.2k · Answer 7 · 2026-04-15 10:35:17

1.2k

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How do I prove this $\int_{0}^{\infty}{e^{-x^n}-e^{-x^m}\over x\ln{x}}dx={\ln{\left(m\over n\right)}}?$

Published on 15 Apr 2026 - 10:35

score 150 · Answer 8 · 2026-04-16 14:34:33

150

Views

Calculate $\int_{-\infty}^{\infty}\frac{\sin(t)}{t}f(t)dt$

Published on 16 Apr 2026 - 14:34

score 271 · Answer 9 · 2026-04-17 00:32:19

271

Views

Evaluate $\int_0^\infty \frac{dx}{x^2+2ax+b}$

Published on 17 Apr 2026 - 0:32

score 59 · Answer 10 · 2026-04-17 11:32:01

59

Views

If the improper integral $\int_{0}^{\infty}f(x)dx$ is covergent.

Published on 17 Apr 2026 - 11:32

score 78 · Answer 11 · 2026-04-11 14:50:23

78

Views

Is this a finite integral?

Published on 11 Apr 2026 - 14:50

score 319 · Answer 12 · 2026-03-25 18:08:14

319

Views

Ways to justify this interchange of summation and integration

Published on 25 Mar 2026 - 18:08

score 1k · Answer 13 · 2026-04-17 15:13:54

1k

Views

Show that $\int_0^1 \left(\left\lfloor\frac{\alpha}{x}\right\rfloor-\alpha\left\lfloor\frac{1}{x}\right\rfloor\right)\mathrm dx=\alpha \ln\alpha$

Published on 17 Apr 2026 - 15:13

score 68 · Answer 14 · 2026-03-27 02:34:12

68

Views

What is the domain for which this integral transform is defined?

Published on 27 Mar 2026 - 2:34

score 140 · Answer 15 · 2026-04-12 22:23:51

140

Views

Integral involving exponential and power

Published on 12 Apr 2026 - 22:23

List Question

Continuity of the improper integral $\int_{0}^{x}y^{-1/2}dy.$

Value of the integral $\int_{a}^{a}f(x)dx?$

Convergence of an improper integral $I=\int_{0}^\infty x^a \ln{(1+\frac{1}{x^2})} dx$

Evaluating $\int_{0}^{\infty}{\sin(x)\sin(2x)\sin(3x)\ldots \sin(nx)\sin(n^{2}x) \over x^{n + 1}}\,dx $

Evaluate$\int_0^1 \frac{x^{m-1} + x^{n-1}}{(1+x)^{m+n}}dx$ in terms of Beta function

Convergence of an improper integral $I=\int_0^\infty \frac{\sin{x}-x\cos{x}}{x^\alpha}dx$

How do I prove this $\int_{0}^{\infty}{e^{-x^n}-e^{-x^m}\over x\ln{x}}dx={\ln{\left(m\over n\right)}}?$

Calculate $\int_{-\infty}^{\infty}\frac{\sin(t)}{t}f(t)dt$

Evaluate $\int_0^\infty \frac{dx}{x^2+2ax+b}$

If the improper integral $\int_{0}^{\infty}f(x)dx$ is covergent.

Is this a finite integral?

Ways to justify this interchange of summation and integration

Show that $\int_0^1 \left(\left\lfloor\frac{\alpha}{x}\right\rfloor-\alpha\left\lfloor\frac{1}{x}\right\rfloor\right)\mathrm dx=\alpha \ln\alpha$

What is the domain for which this integral transform is defined?

Integral involving exponential and power

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