Question

Munkres' definition of the extended integral

score 1k · Answer 1 · 2026-04-02 09:39:05

1k

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Munkres' definition of the extended integral

Published on 02 Apr 2026 - 9:39

score 391 · Answer 2 · 2026-04-16 11:35:44

391

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How to compute $\int_0^{+\infty} \frac{dt}{1+t^4} = \frac{\pi}{2\sqrt 2}.$

Published on 16 Apr 2026 - 11:35

score 216 · Answer 3 · 2026-04-15 20:40:26

216

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Recurrence for $\int \left(\frac{\sin x}{x}\right)^n \, \mathrm{d}x$

Published on 15 Apr 2026 - 20:40

score 85 · Answer 4 · 2026-04-14 14:06:20

85

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Why is this change of variable contradictory?

Published on 14 Apr 2026 - 14:06

score 76 · Answer 5 · 2026-04-12 05:06:51

76

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Evaluate $\int_{-1}^{1}\mathop{dx}\frac{1}{(x^2+a^2)^k}$?

Published on 12 Apr 2026 - 5:06

score 255 · Answer 6 · 2026-04-17 12:19:14

255

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Evaluate integral $\int_{-1}^{1} x^2 \exp(\frac{1}{x^2-1}) dx$

Published on 17 Apr 2026 - 12:19

score 518 · Answer 7 · 2026-04-17 05:00:41

518

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How to evaluate $\int_0^{\pi /2}\frac{u^2\ln{(2\cos u)}}{(u^2+\ln^2{(2\cos u)})^2}du$?

Published on 17 Apr 2026 - 5:00

score 95 · Answer 8 · 2026-04-14 02:07:19

95

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Does $\frac 1 n \int_0^n \frac {g(x)}{h(x)}\,dx\to 0$ if $\int_0^\infty g(x)\,dx$ converges, $\int_0^\infty h(x)\,dx$ diverges and

Published on 14 Apr 2026 - 2:07

score 67 · Answer 9 · 2026-04-15 06:09:35

67

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Am I correctly evaluating the improper integral $\int_9^{\infty} \frac{1}{\sqrt{x^5}} dx$

Published on 15 Apr 2026 - 6:09

score 1.3k · Answer 10 · 2026-04-16 09:54:59

1.3k

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If $\int_{0}^{\infty} f(x) \, dx $ converges, will $\int_{0}^{\infty}e^{-sx} f(x) \, dx$ always converge uniformly on $[0, \infty)$?

Published on 16 Apr 2026 - 9:54

score 135 · Answer 11 · 2026-04-12 08:36:03

135

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Improper integral of trigonometric function

Published on 12 Apr 2026 - 8:36

score 1.1k · Answer 12 · 2026-04-16 13:45:13

1.1k

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Modified Leibnitz integral: $\lim\limits_{a \to\infty}\frac1a\int _0^\infty\frac{(x^2+ax+1)\arctan(\frac{1}{x})}{1+x^4}dx=?$

Published on 16 Apr 2026 - 13:45

score 83 · Answer 13 · 2026-04-14 18:07:50

83

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Compute $\int_0^1 \frac{\exp(u^3 - 4/3 u) du }{\sqrt {1 - u^2}} $

Published on 14 Apr 2026 - 18:07

score 52 · Answer 14 · 2026-04-16 15:30:35

52

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Show $\int_{s}^{\infty} f(x)dx = \mathcal{L} \{\frac{F(t)}{t}\}$ given $f(x) = \int_{0}^{\infty} e^{-xt}F(t)dt$

Published on 16 Apr 2026 - 15:30

score 265 · Answer 15 · 2026-04-14 03:12:51

265

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Riemann integral and Lebesgue integral (in real analysis Folland)

Published on 14 Apr 2026 - 3:12

List Question

Munkres' definition of the extended integral

How to compute $\int_0^{+\infty} \frac{dt}{1+t^4} = \frac{\pi}{2\sqrt 2}.$

Recurrence for $\int \left(\frac{\sin x}{x}\right)^n \, \mathrm{d}x$

Why is this change of variable contradictory?

Evaluate $\int_{-1}^{1}\mathop{dx}\frac{1}{(x^2+a^2)^k}$?

Evaluate integral $\int_{-1}^{1} x^2 \exp(\frac{1}{x^2-1}) dx$

How to evaluate $\int_0^{\pi /2}\frac{u^2\ln{(2\cos u)}}{(u^2+\ln^2{(2\cos u)})^2}du$?

Does $\frac 1 n \int_0^n \frac {g(x)}{h(x)}\,dx\to 0$ if $\int_0^\infty g(x)\,dx$ converges, $\int_0^\infty h(x)\,dx$ diverges and

Am I correctly evaluating the improper integral $\int_9^{\infty} \frac{1}{\sqrt{x^5}} dx$

If $\int_{0}^{\infty} f(x) \, dx $ converges, will $\int_{0}^{\infty}e^{-sx} f(x) \, dx$ always converge uniformly on $[0, \infty)$?

Improper integral of trigonometric function

Modified Leibnitz integral: $\lim\limits_{a \to\infty}\frac1a\int _0^\infty\frac{(x^2+ax+1)\arctan(\frac{1}{x})}{1+x^4}dx=?$

Compute $\int_0^1 \frac{\exp(u^3 - 4/3 u) du }{\sqrt {1 - u^2}} $

Show $\int_{s}^{\infty} f(x)dx = \mathcal{L} \{\frac{F(t)}{t}\}$ given $f(x) = \int_{0}^{\infty} e^{-xt}F(t)dt$

Riemann integral and Lebesgue integral (in real analysis Folland)

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