# Tagged Questions

For questions about problems related to physics that involve evaluating integrals. Purely mathematical questions should be asked at math.SE.

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### When is Lebesgue integration useful over Riemann integration in physics?

Riemann integration is fine for physics in general because the functions dealt with tend to be differentiable and well behaved. Despite this, it's possible that Lebesque integration can be more ...
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### Why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?

I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?
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### Why isn't the Gear predictor-corrector algorithm for integration of the equations of motion symplectic?

Okumura et al., J. Chem. Phys. 2007 states that the Gear predictor-corrector integration scheme, used in particular in some molecular dynamics packages for the dynamics of rigid bodies using ...
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### A basic math identity often used in integrals [closed]

I'm just wondering about why $y_i=A_{ij}x_j$ implies $$d^Ny=|\det A|d^Nx.$$ I see that $\det A$ is the product of the eigenvalues of a diagonal matrix but still don't exactly see how. Please help.
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### What it means to integrate over $n$ variables out of $N$, where $N>n$?

I was reading Theory of Simple Liquids, when I came across BBGKY hierarchy. In deriving the expression for the hierarchy, they integrate an integration of N variables over N-n variables to make the ...
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I'm having trouble with an integral and I would like some pointers on how to "take" it: $$\int \limits_{-\infty}^{\infty}\frac{3\gamma a^{2}d^{3}\mathbf r}{4 \pi \left( r^{2} + \frac{\gamma^{2}}{c^{... 2answers 153 views ### Twistor Function for Coulomb Field In an article by Penrose in Hughston and Ward "Advances in Twistor Theory", it is claimed that the twistor function$$ f(Z^\alpha) = \log{\frac{Z^1Z^2 - Z^0Z^3}{Z^2Z^3}}$$produces an anti-self-dual ... 1answer 129 views ### How is taking the average of an integral over an interval justified? I have been studying classical mechanics. Often when going through a worked problem, I see a step where there is an integral from 0 to 2\pi of \sin^{2} \theta \ d\theta. Instead of using the ... 1answer 102 views ### Question about exterior derivatives I know from Carroll that the integration in GR is basically a mapping from n-form to the real number. And it's given that$$d^nx=dx^0\wedge\ldots\wedge dx^{n-1}=\frac{1}{n!}\epsilon_{\mu_1\ldots\...
Is there a reason why $\int\! d\theta~\theta = 1$ for a Grassmann integral? Books give arguments for $\int\! d\theta = 0$ which I can follow, but not for the former one.
I am working with an operator $\textbf{M}$ that is represented by the Lie group SO(1,3), thus it can be written as, $$\textbf{M} = \exp{\textbf{L}}$$ where,  \textbf{L} = \begin{bmatrix} 0&a&...