List questions from definite-integrals

Published on 13 Apr 2026 - 6:53

117

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To prove that the area lying in the region specified below is $4(4-\pi)$ square units.

Published on 16 Apr 2026 - 16:04

96

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Does $ \int _0^1 \frac{\arctan \left(\frac{x}{x+1}\right)}{\arctan \left(\frac{-2x^2+2x+1}{2}\right)}dx $ exactly equal to $ \frac{1}{2} $?

Published on 14 Apr 2026 - 16:39

196

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$f(x)$ is monotonic , positive, unbounded function then $\int_{0} ^{\infty } f(x)\sin(x)dx$ does not exist

Published on 13 Apr 2026 - 2:19

737

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How do I start this integral problem: $\int_0^1 \frac{\ln^3 u}{1-u} du = -\frac{\pi^4}{15} $?

Published on 14 Apr 2026 - 4:06

73

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What am I doing wrong in this integral?

Published on 11 Apr 2026 - 19:07

3.9k

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What does Infimum of Upper Sum and Supremum of Lower Sums mean?

Published on 15 Apr 2026 - 5:47

396

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$\int_{-\infty}^{\infty} e^{-2ax^2}dx=\frac{\sqrt{\pi}}{\sqrt{2a}}$

Published on 13 Apr 2026 - 21:03

543

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How to calculate Upper/Low sums of an arbitrary partition?

Published on 13 Apr 2026 - 4:44

43

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Using Disc Method to solve Integrand

Published on 11 Apr 2026 - 21:21

430

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Laplace's Method Asymptotic Expansion of an integral

Published on 09 Apr 2026 - 2:01

63

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Compute $\int_{1}^{\infty} e^{2x - x^2}\mathrm dx$

Published on 15 Apr 2026 - 17:22

496

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What is the difference between integrating a work function and a line integral?

Published on 11 Apr 2026 - 7:05

242

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Compute $\int_0^{+\infty}\frac{x^{\alpha}}{1+x^n}dx$, $0<1+\alpha<n$

Published on 16 Apr 2026 - 12:24

562

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Integral $\int_0^2 \frac{\arctan x}{x^2+2x+2}dx$

Published on 16 Apr 2026 - 16:04

List Question

How can I solve this definite integral? 3

To prove that the area lying in the region specified below is $4(4-\pi)$ square units.

Does $ \int _0^1 \frac{\arctan \left(\frac{x}{x+1}\right)}{\arctan \left(\frac{-2x^2+2x+1}{2}\right)}dx $ exactly equal to $ \frac{1}{2} $?

$f(x)$ is monotonic , positive, unbounded function then $\int_{0} ^{\infty } f(x)\sin(x)dx$ does not exist

How do I start this integral problem: $\int_0^1 \frac{\ln^3 u}{1-u} du = -\frac{\pi^4}{15} $?

What am I doing wrong in this integral?

What does Infimum of Upper Sum and Supremum of Lower Sums mean?

$\int_{-\infty}^{\infty} e^{-2ax^2}dx=\frac{\sqrt{\pi}}{\sqrt{2a}}$

How to calculate Upper/Low sums of an arbitrary partition?

Using Disc Method to solve Integrand

Laplace's Method Asymptotic Expansion of an integral

Compute $\int_{1}^{\infty} e^{2x - x^2}\mathrm dx$

What is the difference between integrating a work function and a line integral?

Compute $\int_0^{+\infty}\frac{x^{\alpha}}{1+x^n}dx$, $0<1+\alpha<n$

Integral $\int_0^2 \frac{\arctan x}{x^2+2x+2}dx$

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