# 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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### Lebesgue Integral in physics [duplicate]

I study physics and in this year I have to formule and write my bachelor thesis. I have a lot of ideas but some of them looks more interesting for me. A few days ago I thought about situations in ...
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### How do I evaluate the integral of the square root of a quartic equation? [migrated]

I'm currently trying to evaluate the integral $$\int^1_0 \text{d}t\sqrt{(1-t^2)(1-k^2t^2)}$$ where $k\in(0,1)$. Is it the case that this can be expressed in terms of elliptic integrals? I'm ...
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### How did the equation 1.12 reduced in the given image below? I can't get how the 1/2 factor came into the picture? [closed]

I can't get the solution of W= m/2 integration of d/dt v^2 dt.
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### Finding the work of a non-conservative force [closed]

I need some help with the problem below Calculate the work of the force $\vec{F} = (x^2+yz)\hat{x}+(2y^3-3z)\hat{y}+(-4z+2xy^2)\hat{z}$ from point the point $A(0,0,0)$ to the point $B(1,1,1)$ through ...
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### Is it possble to do this complex symbolic calculation with Matlab? [migrated]

Sorry it's bit abrupt, but recently I am caught up in some symbolic calcualtion which is tedious and almost impossible with mere human hands, so just wondering is it possible to solve the double ...
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### Integration and average in physics? [closed]

Many applications of physics theory involve computations of integrals. Examples are voltage, force due to liquid pressure, surfaces... In some cases, when there is linear dependence between two ...
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### Massive versus Massless $\phi^4$ Sunset Diagram - does $\frac{1}{\epsilon^2}$ term vanish for $m=0$?

In a real scalar massive $\phi^4$-interacting theory consider the amputated sunset diagram. This is the integral out of Kleinert and Schulte-Frohlinde Critical Properties of $\phi^4$-Theories: The ...
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### Hypersurface four-vector, or a familly of four 3-forms?

While reading my old personal notes on forms in relativity, I got confused about some aspects of the mathematical formalism (integration on tensors and p-forms). The energy-momentum flux across some ...
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### Contour integral of Feynman propagator

I am now reading the David Tong's lecture note on Quantum Field theory. I have some questions about the contour used in the integral \begin{equation} \int \frac{d^{4}p}{(2\pi)^{4}} \frac{i}{(p^{0})^{...
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### Torque due to continuous force distribution / pressure [closed]

In my fluid mechanics course, I was exposed to some cases where I need to calculate the torque due to the pressure and all solutions manuals or online tutorials take it as a known fact that $d\tau=rdF$...
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### Commutator of canonical fields in Quantum Field Theory

Let $\phi(\vec{x},t)$ denote the canonical fields and $\pi(\vec{x},t)$ denote the canonical impulses where they're given by: \begin{equation} \phi(x)=\int\frac{d^3\vec{p}}{(2\pi)^3\sqrt{2\omega_{\...
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### Why is $(-\frac{e^2}{4\pi \epsilon_0}) = (-\frac{\hbar ^2}{ma})$?

Note: No, this is NOT a homework question. I am struggling to understand how two physical concepts are related and truly think this could be helpful to a broader audience. Also, I already have the ...
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In the paper "Scattering into the Fifth Dimension of $\mathcal{N}=4$ Super Yang-Mills", the authors give the following result for an integral: \begin{align} I^{(1)}(x_{13}^2,x_{24}^2,m) =& \... 2answers 2k views ### Check dimensions of the integral of a function I and a colleague are arguing about the dimensions of:\int_0^x f(x) dx $$in this particular case [f(x)]=m^2/s^3 and [x]=m. Does it follow that [\int_0^x f(x) dx]=m^2/s^3 or [\int_0^x f(x)... 1answer 27 views ### Torque experienced by a coplanar loop of current in a uniform magnetic field There are a lot of posts on this already, but apparent all of them just consider some special case. I am now struggling with this more general case. Let there be a magnetic field with strength B. ... 2answers 2k views ### Making a cut trough a center of mass, can the masses of the pieces be equal? Let's say point P is the center of mass of an irregularly shaped object. If I make a straight cut trough point P and split the object in two, is it possible for the two pieces to have the same ... 2answers 68 views ### Electric fields in continuous charge distribution My question may be very basic, but I can't think of a reasonable explanation for this. Consider a solid charged sphere. Now, we have an electric field inside the solid sphere, but at any particular ... 1answer 63 views ### Regulating a divergent integral in QED When we try to regulate a divergent integral, we introduce another parameter, say \lambda and then compute the integral. We finally take a limit (either \lambda \rightarrow 0, \infty ) to restore ... 2answers 2k views ### Derivation of Rotational Motion Equations using Calculus How are the equations for rotational motion derived using calculus and the following general equations ?$$\mathbf{v}(t) = \mathbf{v}_0+\int_{t_0}^t \mathbf{a}(t')dt'\mathbf{r}(t) = \mathbf{r}...
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 ...