The integration tag has no wiki summary.
0
votes
0answers
10 views
Is this an exact differential or not? [migrated]
I have the 1-form
$$dz=2xy\, dx+(x^{2}+2y)\, dy$$
And I want to integrate it from $(x_{1},y_{1})$, to $(x_{2},y_{2})$.
If I'm not drunk, checking mixed partials, I find that $dz$ is an exact ...
0
votes
0answers
6 views
Integration of an indefinite integral: matlab precision problem [migrated]
The integral I need to evaluate is:
$$ \int_x^{\infty} \frac{t^n}{e^{t} -1} dt $$
After some research I found a paper saying,
The numerical values of the two integrals [...] are easily ...
1
vote
3answers
65 views
Relation between the time, velocity and acceleration
This is question from I.E. Iredov's General Physics:
$1.22$ : The velocity of a particle moving in the positive direction of the $x-axis$ varies as $v = α \sqrt x$, where $α$ is a positive ...
7
votes
1answer
412 views
I reached a result concerning displacement with quantized time intervals. Am I on to something?
A few days ago, I realized a similarity between distance with constant acceleration, $d = v_i t + 1/2 a t^2$, and the sum of integers up to n, $(n^2 + n)/2$. This came up again today when I decided to ...
6
votes
4answers
124 views
Integrating radial free fall in Newtonian gravity
I thought this would be a simple question, but I'm having trouble figuring it out. Not a homework assignment btw. I am a physics student and am just genuinely interested in physics problems involving ...
4
votes
2answers
111 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 ...
0
votes
1answer
83 views
2
votes
1answer
95 views
Getting rid of double delta function in Feynman rules
[1]
A very simple example of feynman rule for scalar fields.
After computing the diagram i have got the following:
$$
-i(2\pi)^4g^2\int d^4q \frac{i}{q^2 -m^2c^2}\delta^{(4)}(p_1 - p_3 -q)
...
3
votes
2answers
143 views
A four-dimensional integral in Peskin & Schroeder
The following identity is used in Peskin & Schroeder's book Eq.(19.43), page 660:
...
0
votes
2answers
143 views
Calculate the center of mass of a semicircle [closed]
How I determine the center of mass of a semicircle using the definition of center of mass? I only know solve this using the Pappus theorem. Consider that the semicircle is centered on the origin and a ...
-1
votes
3answers
131 views
What needs to be integrated to solve this problem?
An object is placed on a frictionless table with its one end attached to a cord which is connected to a pulley and the tension is maintained constant at 25 N. what is the change in kinetic energy ...
0
votes
1answer
74 views
Change of variables, Fermi Integral
This is a really basic question, but I'm kind of confused.
I have this integral
$$\int_{0}^{\infty}\frac{p^{2}dp}{e^{\alpha+\beta p^{2}/2m}+1}$$
where ...
0
votes
3answers
217 views
Deriving equations of motion using integration
Please refer to my school textbook pg48 (of the book, and not the pdf counter) here: http://ncertbooks.prashanthellina.com/class_11.Physics.PhysicsPartI/ch-3.pdf
My doubt is in this context: (right ...
0
votes
2answers
119 views
Getting position from an accelerometer on an Android phone
I know that integrating acceleration twice will give me position (acceleration-->velocity-->position) but how can I do all this when I all I have are a set of data points (ex: 1 second = some # ...
1
vote
3answers
158 views
Integration by parts to derive relativistic kinetic energy
I have come across a weird integration during derivation of relativistic kinetic energy. Our professor states that i can get RHS out of LHS using integration by parts:
$$
\int\limits_0^x \! ...
3
votes
0answers
110 views
Zeta regularization gone bad
This may sound as a mathematical question, but it should be very familiar to physicists. I am trying to perform an expansion of the function $$f(x) = \sum_{n=1}^{\infty} \frac{K_2(nx)}{n^2 x^2},$$ for ...
2
votes
2answers
50 views
Flux Over a Surface
I am teaching a multivariable calculus course and we are starting to go over surface integrals. I am a math professor with little knowledge of physics. At one point the book discusses fluid flow. ...
5
votes
0answers
116 views
Using $\frac{1}{A+i\epsilon} = PV\frac{1}{A}-i\pi\delta(A)$ in Feynman Integrals
Are the following operations O.K.? This is related to the Feynman parameter trick.
$$F:= \int_0^1 \mathrm{d}x\int_0^{1-x}\mathrm{d}y \frac{1}{f(x,y)+\mathrm{i}\epsilon}.$$ Now using
...
2
votes
1answer
207 views
Crazy Dirac Deltas
I'm not expecting any rigor in the following and the answers...since we're dealing with Dirac deltas in the context of QFT.
Consider the integral
$$
\int d^4q\ \Theta(q_0)\Theta(p_{3,0}+q_0)\ ...
6
votes
1answer
283 views
Loop integral using Feynman's trick
I am trying to show for the one-loop integral with three propagators with different internal masses $m_1$, $m_2$, $m_3$, and all off-shell external momenta $p_1$, $p_2$, $p_3$ the following formula ...
7
votes
4answers
412 views
Possible ambiguity in using the Dirac Delta function
When doing integration over several variables with a constraint on the variables, one may (at least in some physics books) insert a $\delta\text{-function}$ term in the integral to account for this ...
1
vote
1answer
143 views
Shift operator (integral calculus involving Hermite polynomials) [closed]
I didn't know whether to pose this question on Physics.stackexchange or Math.stackexchange. But since this is the last step of a development involving the eigenfunctions of an Harmonic oscillator and ...
2
votes
1answer
229 views
Ashcroft Mermin Solid State Physics Eq. 2.60ff
I'm trying to follow the steps in Eq. 2.60 of said book.
What I cant seem to figure out is how to change the integration variables from 'k' to 'E', as they state.
The equation is
$$\int ...
0
votes
0answers
263 views
Expectation value of a Gaussian wave packet [closed]
How can I compute the expectation value $\langle x\rangle_t$ of a Gaussian wave packet $$\psi(x,t) = \int_{-\infty}^\infty \mathrm dp \, \hat\psi(p) \exp{\frac{-\mathrm i(px - E_p t)}{\hbar}}? $$
...
2
votes
1answer
137 views
Help with Greens function/Fourier transformation to solve screened Poisson equation
I am having trouble getting from one line to the next from this wiki page. I am referring to the text line
Green's function in $r$ is therefore given by the inverse Fourier transform,
where
...
1
vote
2answers
104 views
Are there general circuits that differentiate/integrate empirically?
Is it possible to construct simple circuits, that given a time-varying input, produce an output that represents the derivative or integral of the input with respect to time?
3
votes
0answers
136 views
Should the Jacobian be negative in $\mathrm{d}^4 x$?
In page 24 of Srednicki's QFT textbook, he says that $\mathrm{d}^4x$ is a Lorentz scalar. I understand that the determinant of a Lorentz matrix is always $\pm 1$. So in an improper Lorentz ...
1
vote
1answer
151 views
Integral in Peskin and Schroeder
I'm having a bit of a slow day, and can't see how to do the following integral in Peskin and Schroeder (page 107 for anyone with the book). We've derived in the centre of mass frame the integral over ...
0
votes
0answers
87 views
Nicholas Kollerstrom article on the history of Calculus
Today, Newton´s birthday, I read an article posted in the arXiv by Nicholas Kollerstrom
http://www.arxiv.org/abs/1212.2666
That basically claims that Newton did not invent Calculus. The article does ...
2
votes
2answers
148 views
Gaussian type integral with negative power of variable in integrand
How can we compute the integral $\int_{-\infty}^\infty t^n e^{-t^2/2} dt$ when $n=-1$ or $-2$? It is a problem (1.11) in Prof James Nearing's course Mathematical Tools for Physics. Can a situation ...
2
votes
1answer
236 views
Does the universe obey the holographic principle due to Stokes' theorem?
Does the universe obey the holographic principle due to Stokes' theorem?
\begin{equation}
\int\limits_{\partial\Omega}\omega = \int\limits_{\Omega}\mathrm{d}\omega.
\end{equation}
Can this ...
0
votes
2answers
104 views
Is air drag equation in term of momentum still valid?
This is the known equation of air drag:
$$m{\bf a}=mg-\mathcal D=mg-b{\bf v}.$$
Considering this, is air drag equation in term of momentum still valid?
$$m{\bf v}=mv_g-b{\bf r}.$$
-1
votes
1answer
146 views
What will happen when measuring unmeasurable object?
There is a set called Vitali Set which is not Lebesgue measurable.
Analogously, there also exists a Vitali set $Y$ in $\mathbb R^3$ which is a subset of $[0,1]^3$ and $|Y\cap q|=1$ for all $q\in ...
5
votes
0answers
201 views
Gaussian Integrals : Functional determinant expressed as a trace
Be $A_{ij}$ a symmetric matrix. Then I can easily write
$$
\int \exp\left(-\frac{1}{2}\sum_{i,j}x_i A_{ij} x_j+\sum_{i} B_i x_i\right)\; d^nx=
\sqrt{(2\pi)^n}\exp\left\{-\frac{1}{2}\mathrm{Tr}\log ...
1
vote
1answer
103 views
Gaussian integration and dimension argument
I made a mistake recently regarding the Gaussian density, by putting the determinant of the variance to the power $\frac{d}{2}$. Would the following argumentation be valid to highlight it should be to ...
1
vote
1answer
118 views
What is the definition of density as a function?
(Before I start, I don't know which tag is suitable for this post. Please retag my post if it bothers you.)
Let's say there is a string on $[0,1]$ with a mass given by $m(x)$. ($m(x)$ means the mass ...
1
vote
1answer
299 views
Derivation of the self gravitational potential energy of a sphere
I have been searching on the Internet but have not found a derivation of the formula for the self gravitational potential energy of a sphere. Can someone show how to do this? I assume it involved 6 ...
1
vote
1answer
140 views
Potential for charge distribution, finiteness
Consider a potential for charge distribution:
$$v_H(\mathbf{r}) ~=~ \int \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|}d\mathbf{r'}$$
where $\rho(\mathbf{r'})$ is the charge density.
This ...
1
vote
1answer
98 views
Integration of constant: $\int dp = \Delta p$ in impulse formula
In University Physics, it has something like:
$$\int \sum F dt = \int \frac{dp}{dt} dt = \int dp = \underbrace{p_2 - p_1}_{\Delta p?}$$
But I thought $\int dp = p$? Though my maths is really rusty ...
3
votes
3answers
260 views
How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics?
$$\langle x^2 \rangle = \int_{-\infty}^\infty x^2 |\psi(x)|^2 \text d x$$
What is the meaning of $|\psi(x)|^2$? Does that just mean one has to multiply the wave function with itself?
4
votes
1answer
308 views
A confusion from Weinberg's QFT text (a vanishing term in Lippmann-Schwinger equation)
I was reviewing the first few chapters of Weinberg Vol I and found a hole in my understanding in page 112, where he tried to show in the asymptotic past $t=−∞$, the in states coincide with a free ...
2
votes
0answers
87 views
What is the correct way of integrating in astronomy simulations? [closed]
I'm creating a simple astronomy simulator that should use Newtonian physics to simulate movement of plants in a system (or any objects, for that matter). All the bodies are circles in an Euclidean ...
3
votes
3answers
306 views
Why we use $L_2$ Space In QM?
I asked this question for many people/professors without getting a sufficient answer, why in QM Lebesgue spaces of second degree are assumed to be the one that corresponds to the Hilbert vector space ...
1
vote
1answer
129 views
dimensional analysis of Grassmann integration/differentiation
There is another paradox that I need to resolve:
The Berezin integration rules for Grassmann odd variables give the same result as differentiation:
If $f=x+\theta\psi$ is a superfunction, the ...
1
vote
1answer
151 views
Questions regarding solving the Brachistochrone problem using Lagrangian
brachistochrone problem: Suppose that there is a rollercoaster. There is point 1 ($0,0$) and point 2 ($x_2, y_2)$. Point 1 is at the higher place when compared to the point 2, so the rollercoaster ...
1
vote
0answers
164 views
Integrals given by Landau [closed]
Discussion about Landau's "Theoretical Minimum" has already been posted here. Unfortunately I couldn't find much about some examples of questions he gave to students. There are three questions in the ...
12
votes
3answers
445 views
When is Lebesque 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 ...
2
votes
1answer
1k views
Determining the center of mass of a cone
I'm having some trouble with a simple classical mechanics problem, where I need to calculate the center of mass of a cone whose base radius is $a$ and height $h$..!
I know the required equation. But, ...
6
votes
2answers
298 views
What the circled integral?
What the circled integral
$$
\oint
$$
means?
I saw this symbol in a lot of books about advanced physics.
How is his definition? What kind of integral it is? It is used only in physics or also in ...
4
votes
4answers
561 views
How do you do an integral involving the derivative of a delta function?
I got an integral in solving Schrodinger equation with delta function potential. It looks like
$$\int \frac{y(x)}{x} \frac{\mathrm{d}\delta(x-x_0)}{\mathrm{d}x}$$
I'm trying to solve this by ...
