Question

Conversion of proper to improper integrals and vice versa, is the following case possible?

score 42 · Answer 1 · 2026-04-12 10:10:13

42

Views

Conversion of proper to improper integrals and vice versa, is the following case possible?

Published on 12 Apr 2026 - 10:10

score 170 · Answer 2 · 2026-04-16 17:03:21

170

Views

Calculation of improper integral: $\int_{0}^{\infty}\frac{x^3\ln x}{(x^4+1)^3} \,dx$

Published on 16 Apr 2026 - 17:03

score 66 · Answer 3 · 2026-04-16 13:20:43

66

Views

Is $J(y)= \int_{[1, \infty)} \exp(\frac{-1}{y^2}(x-\frac{1}{y})^2) \, dx$ uniformly convergent on $(0,1)$?

Published on 16 Apr 2026 - 13:20

score 104 · Answer 4 · 2026-04-17 05:53:25

104

Views

Why does $\left(\int_{-\infty}^{\infty}e^{-t^2} dt \right)^2= \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-(x^2 + y^2)}dx\,dy$?

Published on 17 Apr 2026 - 5:53

score 1k · Answer 5 · 2026-04-17 08:52:10

1k

Views

Looking to solve an integral of the form $\int_1^\infty (y-1)^{n-1} y^{-n} e^{(\alpha -\alpha n)\frac{(y-1) }{y}} \; dy$

Published on 17 Apr 2026 - 8:52

score 2.3k · Answer 6 · 2026-04-11 07:57:14

2.3k

Views

How to calculate the average x-coordinate of a region?

Published on 11 Apr 2026 - 7:57

score 531 · Answer 7 · 2026-04-17 06:10:25

531

Views

Compute $\int_{0}^{1} \frac{\ln(x)}{(x+1)^2} \mathrm dx$

Published on 17 Apr 2026 - 6:10

score 650 · Answer 8 · 2026-04-15 14:25:03

650

Views

use the definition of an improper integral to evaluate the given integral.$\int_3^\infty\frac{1}{(x+2)}dx$

Published on 15 Apr 2026 - 14:25

score 158 · Answer 9 · 2026-04-15 22:25:25

158

Views

About the volume of the graphics of $f(x)=\frac{\sin(x)}{x}$ revolved around the $x$-axis.

Published on 15 Apr 2026 - 22:25

score 298 · Answer 10 · 2026-04-15 18:07:57

298

Views

Closed form of $\lim\limits_{n\to\infty}\left(\int_0^{n}\frac{{\rm d}k}{\sqrt{k}}-\sum_{k=1}^n\frac1{\sqrt k}\right)$

Published on 15 Apr 2026 - 18:07

score 68 · Answer 11 · 2026-04-18 02:53:43

68

Views

Integral $\frac{x^{1/4} }{ x^{1/2}-1}$ dx

Published on 18 Apr 2026 - 2:53

score 352 · Answer 12 · 2026-04-12 11:12:28

352

Views

Complicated definite integral involving exponential and trig function

Published on 12 Apr 2026 - 11:12

score 687 · Answer 13 · 2026-03-25 22:10:04

687

Views

Cauchy principal value for solving the integral of complex exponential

Published on 25 Mar 2026 - 22:10

score 301 · Answer 14 · 2026-04-11 14:37:46

301

Views

Integration and evaluation

Published on 11 Apr 2026 - 14:37

score 558 · Answer 15 · 2026-04-15 23:15:55

558

Views

If $[a,b]$ is an interval of minimal length with $\int_a^bf(x)dx=\alpha$ then $f(a)=f(b)$

Published on 15 Apr 2026 - 23:15

List Question

Conversion of proper to improper integrals and vice versa, is the following case possible?

Calculation of improper integral: $\int_{0}^{\infty}\frac{x^3\ln x}{(x^4+1)^3} \,dx$

Is $J(y)= \int_{[1, \infty)} \exp(\frac{-1}{y^2}(x-\frac{1}{y})^2) \, dx$ uniformly convergent on $(0,1)$?

Why does $\left(\int_{-\infty}^{\infty}e^{-t^2} dt \right)^2= \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-(x^2 + y^2)}dx\,dy$?

Looking to solve an integral of the form $\int_1^\infty (y-1)^{n-1} y^{-n} e^{(\alpha -\alpha n)\frac{(y-1) }{y}} \; dy$

How to calculate the average x-coordinate of a region?

Compute $\int_{0}^{1} \frac{\ln(x)}{(x+1)^2} \mathrm dx$

use the definition of an improper integral to evaluate the given integral.$\int_3^\infty\frac{1}{(x+2)}dx$

About the volume of the graphics of $f(x)=\frac{\sin(x)}{x}$ revolved around the $x$-axis.

Closed form of $\lim\limits_{n\to\infty}\left(\int_0^{n}\frac{{\rm d}k}{\sqrt{k}}-\sum_{k=1}^n\frac1{\sqrt k}\right)$

Integral $\frac{x^{1/4} }{ x^{1/2}-1}$ dx

Complicated definite integral involving exponential and trig function

Cauchy principal value for solving the integral of complex exponential

Integration and evaluation

If $[a,b]$ is an interval of minimal length with $\int_a^bf(x)dx=\alpha$ then $f(a)=f(b)$

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