# Questions tagged [integration]

Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...

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### Polya-Laguerre Class and inversion formula

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### Interchange of integration and supremum

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### $\int\limits_{-\infty}^\infty \left(f(\frac{x-\mu}{1+\Psi/2})-f(\frac{x+\mu}{1-\Psi/2})\right)\frac{x\gamma}{(x-x_{0})^{2}+a}dx$

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### Estimate of $\frac{\int x^{2p}\,e^{-x^{2n}\,+\,\omega(x,y)}\;dx}{\int e^{-x^{2n}\,+\,\omega(x,y)}\;dx}$

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### Green's identity with a different norm

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### Ratios of Gaussian integrals with a positive semidefinite matrix

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### On integral representation of Whittaker $W$ functions

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### On integral relating logarithmic of absolute value of Zeta function:

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### Derivatives of $G_h(u):=\int_0^{2\pi} h(\cos t)h(\cos(t - \arccos(u)))dt$ when $h$ is positive-homogeneous

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### On the Bochner spaces $L^\infty(a,b;L^p(c,d))$ and $L^p(c,d;L^\infty(a,b))$, or: Interchange of supremum and integral

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### Sufficient conditions for finite mean of a non-negative random variable

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### Is integration against an indicator Wasserstein-Continuous

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### Riemann-Stieltjes integral of a distribution function

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### Decide the order of of an integration involving the $\log$ function

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### Generalized Selberg integral

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### How does the area affect the integral?

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### Which units describe the area under a curve? [migrated]

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### The loss of double periodicity (ellipticity)

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### Integrals involving fractions of exponentials

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### 'Partial Integral' Equation

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### Faster than Euler's substitution. How to derive this formula?

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### Which averages of products of a function give a norm?

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### The many theories of integration

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### definite integral with incomplete gamma function and exponential

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### Laplace transform calculation

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### A possible error in Villani's monograph “Hypocoercivity”

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### van Cittert deconvolution method

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### Help with a limit involving incomplete beta integral

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### Generalizing contour integration to quaternions and bicomplex numbers

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### Question on an exercise from Terry Tao's blog

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### Sources for multiple Stieltjes integral

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### A tricky integral to evaluate

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### Integration of fractional function over Rice distribution

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### integral of fractional function

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### Trying to evaluate an integral relating to $\zeta (3)$

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### Expected distance between two uniform points in distinct rectangles

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### Length of isoline $x(1-x)y(1-y)=c$

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### Decoupling a double integral

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### How to find or approximate (e.g. using method of steepest descent ) integral?

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### Integrating multinomial likelihood over intersection of two simplexes

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### Distribution of $\sqrt{X^2+Y^2}$ when $X$ and $Y$ are Cauchy

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### Asymptotic of an improper integral

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### Is $\iiint_{[0, 1]^3} \lvert f(x)+f(y)+f(z)\rvert\, dx\, dy\, dz \ge \int_0^1 \lvert f(x)\rvert\, dx$?

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### How does one interpret the wetting area?

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### Wiener-Hopf Factorization: How are these contour integrals done?

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### Fundamental Theorem of Algebra via multiple integrals

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### Multivariate gaussian integral

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### Integration by parts with fractional Laplacian and divergence

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### Injectivity of an integral transform

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