# Questions tagged [integration]

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

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### What is the role of constant in 1st equation of motion [closed]

In the proof of the equation of motion , while we integrate both sides.so, the constant is produced on both sides which cannot be always same then what about the constant in the equation
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### Why can't we find electric field of a uniformly charged hollow hemisphere by using vertical strips which are perpendicular to the flat surface? [closed]

I tried finding electric field of hollow hemisphere by using integration on vertical strips which are at angle theta but the answer comes wrong but I get the answer when I integrate horizontal strip? ...
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### Confusions on The Gravitational Energy of a Point P in a Cube

I have been working, quite tirelessly, to try and find an answer to a question that has been bothering me for some time now. I have been working over some proofs, in the Newtonian Mechanics world, to ...
64 views

### Net particle number density for relativistic particles at finite chemical potential (tricky integral)

Question: How does one show that the chemical potential of relativistic fermions is negligible at high energies? In particular, I would like to show that the difference between the particle density $n$...
196 views

### How to use a piecewise acceleration function to get a position function?

This should be a relatively easy problem but I think I am missing something somewhere. This problem consists of a object that is being thrown into the air at $t = 4s$ at a velocity $v_0$ here is my ...
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### $p(z)$ polynomial with $p(0) \neq 0 \neq p(1)$; $\int_{\partial R} \frac{p(z)}{(z-1)z^2}dz$; $R=[-1,2] \times [-1,3]$ [migrated]

Consider $p(z)$ a polynomial such that $p(0) \neq 0 \neq p(1)$ and the rectangle $R=[-1,2] \times [-1,3]$, calculate $\int_{\partial R} \frac{p(z)}{(z-1)z^2}dz$ The poles $P=\{0,1\}$ are in the ...
100 views

### What does the superscript $3$ in $d^3x$ mean in an integral?

At the risk of seeming ignorant, please explain what does the superscript $3$ in $d^3x$ mean in the integrals 5.12, 5.13, 5.14, 5.15? Why 3? Why there is no such in the 5.10 integral?
311 views

### Do we put negative sign while calculating inward flux by Gauss Divergence theorem?

Suppose we have a vector field $\vec A=ax\hat i + by\hat j+cz\hat k$ and we want to calculate its inward flux $\int \vec A\cdot\vec {dS}$ over the spherical surface $x^2+y^2+z^2=1$(with area vector ...
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### Trick for integration into a plane wave basis

I'm reading the article https://arxiv.org/abs/hep-th/9705200 and part of it has left me very confused. In order to speak about their equation (1) the authors make the following statement: \begin{align*...
52 views

### Difference of $p^0$ and $E_p$

In QFT when I learn about Feynman-propagator, I see such an expression: $$\frac{1}{2E_p}e^{-iE_p(x^0-y^0)}=-\frac{1}{2\pi i}\int_Cdp^0\frac{e^{-ip^0(x^0-y^0)}}{(p^0-E_p)(p^0+E_p)}.$$ I know that ...
1 vote
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### Proof for Moment of Inertia of Triangle (with respect to the axis out of the page at a origin) [duplicate]

I found a formula for a "Triangle with vertices at the origin and at $P$ and $Q$, with mass $m$, rotating about an axis perpendicular to the plane and passing through the origin" given on ...
1 vote
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### How to Find Trajectory of Particle?

Let’s say I have a particle, and I know all the forces acting on it at every position. (Let’s say the particle is in an electric/gravitational field to simplify the mathematics involved.) Now, is ...
1k views

### Finding the illuminance from a triangular light source

Since most light sources in games are point-like, it's pretty difficult to approximate area light sources with point sources. As triangles are a universal form to represent 3D models (thus area light ...
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### Second-Order Perturbation Correction for Helium atom

I am trying to calculate the second order perturbation correction for helium atom: $$E^{(2)}_n = \sum^\infty_{i, i \neq n} \frac{|\langle \Psi_n | V | \Psi_i \rangle|^2}{E_n - E_i}$$ with the ...
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### When can I commute the 4-gradient and the "space-time" integral?

Let's say I have the following situation $$I = \dfrac{\partial}{\partial x^{\alpha}}\int e^{k_{\mu}x^{\mu}} \;d^4k$$ Would I be able to commute the integral and the partial derivative? If so, why is ...
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### How do I integrate the Maxwell-Boltzmann-Distribution in terms of the 4-velocity?

I want to calculate the interaction rate of a 2->2 process where the distribution function of the particles is given by the Maxwell-Boltzmann distribution. The result has already been published in ...
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1 vote
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### Why can we do Wick rotations even if $\Delta<0$?

The above page is from Schwartz QFT. Why can we do Wick rotations even if $\Delta<0$?
1 vote
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### Integral of Theta function [closed]

I'm trying to compute the following integral, useful to calculate Amplitudes in String theory \int \frac{d^2z}{\tau_2} \;\partial^2_z \log \vartheta_1\left(z\right) = - \frac{\pi}{\...
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### Residue theorem application

First I want to provide a little bit of context: I finished my undergrad degree in physics in 2008 and after that I moved into strategic consulting and into the financial world. Right now, at 41 years ...
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### Hooke's law and derivation of work done by spring confusion

For simplicity I'll do this in 1 direction so I can let the sign dictate direction and ditch the vector notation. The force done by a spring can be written as $$F = -k\Delta x ,$$however this ...
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### How to know the position of an object when calculating the center of mass, without using integrals? [closed]

For example, if I have a 1/4 piece of pizza, what is the position?
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### Exponential decay of propagator outside lightcone

In Tong's lecture notes (http://www.damtp.cam.ac.uk/user/tong/qft.html) page 38, he calculates the following propagator: D(x-y) = \int \frac{d^3 p}{(2\pi)^3} \frac{1}{2E_\vec{p}} e^{-ip \cdot (x-y)}....
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Let's consider the orthonormality condition for an eigenfunction $\Psi_p(x)=(2 \pi \hbar)^{1/2}e^{\frac{i}{\hbar} px}$ (plane wave) of the momentum operator with eigenvalue $p$. Then the ...