List questions from integration

Published on 16 Apr 2026 - 15:05

86

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Let $f(x)=\frac{\arctan(x)}{x}$. Let $F$ be the anti-derivative of $f$ in $\mathbb{R}$. Prove $F$ is not bounded above in $\mathbb{R}$.

Published on 16 Apr 2026 - 18:35

445

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Calculate $\int_{\mathbb R^3} \exp(-x^tAx + b^tx) \,\lambda_3(dx)$

Published on 09 Apr 2026 - 0:04

45

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Volume of a Solid of Rotation Without Shells

Published on 09 Apr 2026 - 1:56

74

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How to calculate the residue of this function with this rectangle contour?

Published on 14 Apr 2026 - 9:59

2.5k

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How would one integrate this: $\int xdy$, where y is a function of x?

Published on 13 Apr 2026 - 10:18

273

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How can one solve this integral analytically?

Published on 09 Apr 2026 - 2:27

75

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Solution to integral equation involving logarithms

Published on 09 Apr 2026 - 0:02

66

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Integration by substitution and root of unity

Published on 18 Apr 2026 - 5:03

177

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Justify an approximation of $\sum_{k=1}^\infty\operatorname{Ei}(-k)$, where $\operatorname{Ei}(x)$ denotes the exponential integral function

Published on 12 Apr 2026 - 20:19

2.2k

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Volume Using Integration

Published on 09 Apr 2026 - 5:00

598

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MIT Integration Bee $21$

Published on 15 Apr 2026 - 13:13

1.3k

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Integral $\int \:\frac{dt}{\left(t^2-1\right)^2}$

Published on 06 Apr 2026 - 10:36

46

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Volume of Solid W/ Base Region...

Published on 13 Apr 2026 - 23:26

3.7k

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Volume with Cross Sections Perpendicular to Y-Axis

Published on 13 Apr 2026 - 9:48

List Question

Integrate $\int \frac{2x+7}{(x+1)(x^2+1)}dx$.

Let $f(x)=\frac{\arctan(x)}{x}$. Let $F$ be the anti-derivative of $f$ in $\mathbb{R}$. Prove $F$ is not bounded above in $\mathbb{R}$.

Calculate $\int_{\mathbb R^3} \exp(-x^tAx + b^tx) \,\lambda_3(dx)$

Volume of a Solid of Rotation Without Shells

How to calculate the residue of this function with this rectangle contour?

How would one integrate this: $\int xdy$, where y is a function of x?

How can one solve this integral analytically?

Solution to integral equation involving logarithms

Integration by substitution and root of unity

Justify an approximation of $\sum_{k=1}^\infty\operatorname{Ei}(-k)$, where $\operatorname{Ei}(x)$ denotes the exponential integral function

Volume Using Integration

MIT Integration Bee $21$

Integral $\int \:\frac{dt}{\left(t^2-1\right)^2}$

Volume of Solid W/ Base Region...

Volume with Cross Sections Perpendicular to Y-Axis

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