List questions from definite-integrals

Published on 10 Apr 2026 - 23:02

250

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How to evaluate $\int_{0}^{1}\arccos\sqrt{1-x}\ln(x-x^2)\ln\left(\frac{1}{x}-1\right)dx?$

Published on 16 Apr 2026 - 5:13

185

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Does an integrable function have to have a point of continuity?

Published on 10 Apr 2026 - 19:55

64

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Question about path integral over unit circle

Published on 08 Apr 2026 - 22:53

397

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Interesting integral of $\frac {\log x}{\sqrt{1-x^2}}$

Published on 16 Apr 2026 - 12:15

136

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Find the continuous function defined over $[0,1]$ such that $\int_0^1f(x){\rm d}x=1, \int_0^1 xf(x){\rm d}x=a$ and $\int_0^1x^2f(x){\rm d}x=a^2 .$

Published on 16 Apr 2026 - 17:26

149

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Centre of mass of a region in the polar plane

Published on 14 Apr 2026 - 2:35

166

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Why is this integral equal to zero?

Published on 14 Apr 2026 - 23:09

54

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Calculate the integral of $f(x,y,z)=12xyz$ on $D=\{ (x,y,z) \in R^3 \mid 0<x,y, \text{ and } \sqrt{2}(x^2+y^2)<z<\sqrt{3-x^2-y^2})\}$

Published on 15 Apr 2026 - 23:32

161

Views

Is $\vec{F}\cdot \hat{n}$ zero on the boundary?

Published on 15 Apr 2026 - 5:29

403

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Finding closed form of $\int_{-\infty}^{\infty}\frac{dx}{x^{2n}+1}$

Published on 14 Apr 2026 - 23:22

1k

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Recreational math: If $f(f(x))=e^x$, bound the integral $\int_0^1 f(x)dx$

Published on 16 Apr 2026 - 14:51

192

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Integrating integer powers of $\cos(\theta)$

Published on 11 Apr 2026 - 6:20

262

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Solve $\int \frac{2x}{(x^2+x+1)^2}dx$

Published on 17 Apr 2026 - 10:32

182

Views

Integration of $ \int_1^2 \frac{3x^3 + 3x^2 - 5x + 4}{3x^3 - 2x^2 +3x -2} \mathrm dx$

Published on 16 Apr 2026 - 14:34

List Question

Finding upper and lower sum of a Heaviside function.

How to evaluate $\int_{0}^{1}\arccos\sqrt{1-x}\ln(x-x^2)\ln\left(\frac{1}{x}-1\right)dx?$

Does an integrable function have to have a point of continuity?

Question about path integral over unit circle

Interesting integral of $\frac {\log x}{\sqrt{1-x^2}}$

Find the continuous function defined over $[0,1]$ such that $\int_0^1f(x){\rm d}x=1, \int_0^1 xf(x){\rm d}x=a$ and $\int_0^1x^2f(x){\rm d}x=a^2 .$

Centre of mass of a region in the polar plane

Why is this integral equal to zero?

Calculate the integral of $f(x,y,z)=12xyz$ on $D=\{ (x,y,z) \in R^3 \mid 0<x,y, \text{ and } \sqrt{2}(x^2+y^2)<z<\sqrt{3-x^2-y^2})\}$

Is $\vec{F}\cdot \hat{n}$ zero on the boundary?

Finding closed form of $\int_{-\infty}^{\infty}\frac{dx}{x^{2n}+1}$

Recreational math: If $f(f(x))=e^x$, bound the integral $\int_0^1 f(x)dx$

Integrating integer powers of $\cos(\theta)$

Solve $\int \frac{2x}{(x^2+x+1)^2}dx$

Integration of $ \int_1^2 \frac{3x^3 + 3x^2 - 5x + 4}{3x^3 - 2x^2 +3x -2} \mathrm dx$

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