Questions tagged [integration]

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

713 questions
Filter by
Sorted by
Tagged with
59 views

Can I use dimensional regularization with this integral?

I would like to extract the divergence of this integral in 4d Euclidean space: $$\int d^4z \frac{1}{(x-z)^4}\tag{1}$$ This divergence is expected to cancel with other divergences, which I got using ...
51 views

Why is this equation correct?

This problem seems to be solved the exact same way in multiple solution books, so I'm certain that the way it is done is correct and that I'm just rusty when it comes to calculus due to multiple years ...
95 views

When can I set $d=4$ in dimensional regularization?

I am using dimensional regularization to extract the divergence of some complicated integral. I work in $d=2\omega$ dimensions, with $\omega\approx 2$. After I extract the divergence, I have an ...
85 views

How to solve integrals with $3$ Feynman parameters? [migrated]

I would like to evaluate integrals of the following type (in position space): $$\int \frac{d^{2\omega}z}{\left[(x_1-z)^2 (x_2-z)^2 (x_3-z)^2 \right]^A} \tag{1}$$ I can introduce three Feynman ...
39 views

Work done to compress a liquid in container [closed]

Into a compressed container containing water with pressure p and volume V we want to pump additional water. What is the work done? Unlike in the ideal gas, the work cannot be simply found out using ...
42 views

Integrating a product of Gaussian distributions

I'm stuck at this relatively easy looking integral where I have gaussian distributions \begin{equation} \sigma(x,y)=\frac{1}{\sqrt{2\pi\sigma^2}} e^{-\frac{x^2+y^2}{4\sigma^2}} \end{equation} and the ...
100 views

Suppose we want to find the electrostatic potential $\phi_{0}$, with reference to infinity, at $r_{0}$ resulting from a positive charge $q$ located at the origin. For simplicity, let us assume we are ...
60 views

Evaluation of contour integration [closed]

Consider the integral $\int^{\infty}_{-\infty}\frac{q\exp(iqR)}{q^2-k^2}dq$. This kind of equation appears in evaluation of Green's function in scattering theory.We use contour integration to evaluate ...
68 views

Find velocity from acceleration equation [closed]

Suppose the acceleration of a particle is a function of $x$, where $$a(x) = (2.2 s^{-2})x$$ (a) If the velocity is zero when x = 1.0 m, what is the speed when x = 3.4 m? (b) How long does it take ...
71 views

What am I not understanding about this double integration of acceleration to get position?

Brilliant.org has a module on classical mechanics and I'm having difficulty with a mathematical step. They want you to represent position in terms of acceleration and then to solve the double integral ...
323 views

Help on a hard integral [migrated]

So, I'm doing an extensive homework of electromagnetism and we are searching for the total electromagnetic angular momentum of the Thomson dipole. In the end, there is one integral we cannot solve. By ...
14 views

“Euclid’s test” , Negative Pressure and Measure Theory

I don't understand what does it mean for 'Euclid's Test' when they talk about negative pressure Using Euclid’s test for a hypothesis of examining its implications, one finds that negative pressure ...
46 views

Monte Carlo integration - convergence

I have a 5D integral being calculated with a Monte Carlo uniform random sampling. The issue is that the region of integration is very small and for 100000 points I get only around 20-30 points every ...
96 views

A triple integral in Spherical coordinates from Jackson's book on Electrodynamics [closed]

I have been trying a solution for the following integral from Jackson but i do not seem to go anywhere. Please help. The problem is to compute interaction energy due to 2 charges. Compute following ...
50 views

Oscillator integral for frequency

If, for a (not necessarily simple harmonic) oscillator I have that $$\frac{dx}{dt} = G(x)$$ then I can express the period of motion as $$\int_{0}^{T/4} dt = \int_{0}^{X_{max}} \frac{dx}{G(x)}.$$ What ...
53 views

Area under a velocity graph

If I took the definite integral of a velocity graph from 0 to 10 seconds, the answer would be the change in position over those 10 seconds correct? I am told by my teacher the area is change in ...
52 views

Gaussian oscillatory integral evaluation using regularization

To evaluate the Gaussian integral $$\int_{-\infty}^\infty dx e^{iax^2} = \sqrt{\frac{\pi i}{a}},$$ one can use an appropriate contour as here, or use the method of "regularization", contained for ...
45 views

55 views

88 views

88 views

Gaussian wave packet with a step potential

In principle of quantum mechanics by Shankaar on page 170, while doing transmission and reflection index for a step potential for a Gaussian wave packet moving to the right. We come to this ...
44 views

32 views

Constant Acceleration and Displacement

How can I conduct an experiment to show that the area under a velocity-time graph equals the displacement when the velocity is changing at a constant rate? I've tried to measure free falling objects, ...
28 views

Finding suitable element to perform integration upon [closed]

Is there any precise (proper) method or technique to specify the element on which integration will be performed. Is it the same for all properties like moment of inertia, gravitational potential, ...
29 views

Total amount of diffusely reflected light off of a sphere?

I have a numerical simulation that uses ray tracing to calculate the total amount of light picked up by a sensor, after diffusely reflecting off of an object. To validate this simulation, I'd like to ...
227 views

Showing $I=\int d^3k\int dk^0\frac{1}{k^4}$ to be logarithmically divergent

Consider a momentum integral of the form $$I=\int d^3k\int dk^0\frac{1}{k^4}$$ where $k^2=(k^0)^2-(\vec{k})^2$ and the integral over $k^0$ runs from $-\infty$ to $+\infty$. This integral is common in ...
23 views

Units after integrating a ratio metric: Point Source Transfer Mobility

I want to calculate the so called Line Source Transfer Mobility (LSTM) from 10 equispaced Point Source Transfer Mobilities (PSTM). The PSTM measures the response to an excitation, and it is defined ...
61 views

Fractional Fourier Transform and Fresnel Propagation

I am currently trying to wrap my head around Fresnel propagation, and I understand it is mathematically linked to the Fractional Fourier Transform, but I'm having a hard time with the units and the ...
61 views

Direction of integration and boundary limits in electromagnetism?

I have encountered several problems regarding the choice of direction of integration and the boundary limits, this semester in electromagnetism. Is there some rule, so I don't do it wrong again. In ...
A plane wave scattered by a 1D potential can be described by, $$\psi(x) = \begin{cases} e^{ikx} + R e^{-ikx}, & x<0\\ T e^{ikx}, & x>0 \end{cases}$$ where $R$ is the reflection ...