# 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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### Cauchy's Integral with quadratic exponential term [migrated]

As I was studying the Cauchy's integral formula, I tried to do the integral: \begin{equation} I = \int_{-\infty}^{\infty} \frac{1}{x - a} e^{(i A x^2 + i B x)} dx \end{equation} with $A>0, B>0$ ...
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### Kinetic theory: Computing the flux density

The problem is the following: Set up: A sealed box contains a collisionless classical gas of particles, each of mass $m$. The box is coupled to a thermostat such that interactions between particles ...
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### Recasting integrals from Lagrangian to Eulerian frame

Working on a research problem in the continuum mechanics of fluids. For clarity, uppercase will be used for tensors in the reference configuration, and corresponding spatial items will be in lowercase....
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### Maxwell model subject to reversing constant strain rate

I've been reading about viscoelastic models and using Excel to plot some of their characteristics. I'm particularly interested in their response to a constant strain rate which reverses periodically ...
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### Does changing the direction of paths change the value of the path-integral?

When we use path-integral formalism to calculate some quantities, we often specify the starting and the ending points in the phase space, say $A$ and $B$. Let say $\gamma_A^B$ denote a path that ...
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### What are some areas of physics, where the concept of “natural integral” may arise?

Natural integral (as we will define it) is a distinguished antiderivative of a function that can be understood as interpolation of the sequence of consecutive derivatives to the $-1$. It has a ...
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### Is the average force calculated from $F(x)$ the same as that calculated from $F(t)$?

Say a force is doing work on an object in one dimension. I could calculate the average force over the distance with $$\frac{1}{\Delta{x}}\int_{x_1}^{x_2} F(x) \text dx$$ If I also formulated force ...
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### Understanding the differential in integrals

After years, I still find myself having trouble really internalizing the meaning of various differentials in integrals—specifically, when they come about via reasoning regarding physical phenomena. ...
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### Limits of Integration Trig, Mag Field Infinite Length Wire

I don't understand how the limits of integration should be defined when doing basic integrals of trig functions. It seems like it's an arbitrary decision, I don't understand it. Here's the set up: ...
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### Product over integral representations and steepest descents

Suppose we have a product of Dirac or Heaviside functions in the context of a spin model and we use an integral representation to express these in order to do some manipulations, more specifically ...
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### Work done by electric force when moving like charges together

Consider two positive charges. I would like to find the work done by the electric force on charge +q as it is brought closer to charge +Q from radius a to b. I first define electric force as a ...
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### Moment of inertia and centre of masses of continuous bodies [duplicate]

I'm quite accustomed with integration and all those calculus involved in finding moment of inertia as well as center of mass. But a random thought is wiggling in my mind. Why do we take $dm$ instead ...
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### Density of states (DOS) integral when surface is not closed

According to the density of states (DOS) formula $$\rho(\varepsilon)\propto \int_{\varepsilon=\text{const}}\frac{dS}{|\nabla_k \varepsilon_k|}.$$ Since there is an integral on the constant energy ...
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### $dE$ stands in my way to know the density of states in bulk crystal, how to get rid of it?

In a book about semiconductors, I found the following formula for the density of states: $$D(E)dE=\frac{(2m)^{3/2}E^{1/2}}{2\pi^2\hbar^2}dE. \tag{1}$$ In that book, the important lesson from this ...
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### Electric field of given charge density

Given the charge density $$\rho(\vec{x})=\rho_0\delta(x_1)\delta(x_2),$$ where $\delta$ denotes the Dirac-distribution and $\vec{x}=(x_1,x_2,x_3)$, I am asked to calculate the electric field which is ...
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### $\oint{A}=0\implies$ A is a State function?

If $A$ is a thermodynamic variable (ex:Pressure, volume, entropy). then If $\oint{A}=0$, then does it imply that $A$ has to be a state function? I'm trying to prove that Entropy is a state function. ...
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### Finding rate of change of momentum in a fire extinguisher [closed]

I am trying to find the rate of change of momentum as asked by part ii. I have begun the question by saying "dp/dt= -dN/dt x momentum of a particle". To cancel out the sqrt(pi) factor in dN/dt it ...