# Questions tagged [integration]

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

853 questions
Filter by
Sorted by
Tagged with
45 views

16 views

### Fetter and Walecka's derivation of perturbation theory of imperfect fermi gas

I've been learning the imperfect fermi gas, in Chapter 4 of Fetter & Walecka's book on Many-Body Physics. I have a hard time with one integral, equation (11.62) in P145. From this integral we can ...
31 views

### Closed form solution of the normal density of a superfluid for the Bogoliubov spectrum

I've been trying to solve the following definite integral $$\int_0^\infty dx\, x^4\, \frac{e^{\sqrt{x^4+2 x^2}/Tp}}{\left(e^{\sqrt{x^4+2 x^2}/Tp}-1\right)^2}\, ,\quad Tp = \frac{T}{Un}$$ This is the ...
67 views

### Closed form solution to normal fluid density integral in the two fluid model [migrated]

I've been trying to solve the following definite integral $$\int_0^\infty dx\, x^4\, \frac{e^{x^2+a}}{\left(e^{x^2+a}-1\right)^2}\quad , \qquad a>0\, .$$ This is the density of the normal part of ...
24 views

### Contour Integration in Mathematica [migrated]

I need to solve an integral similar to following for a project: \begin{equation} F[p^2\_,q^2\_]\equiv\int_0^{\infty}dk\, e^{-k/\lambda}\, \frac{k}{k-b[p^2,q^2]- I\epsilon}\ln(k-b[p^2,q^2]) \end{...
63 views

### Alternate way to calculate an integral

There's an infinite wire carrying current I on the origin along the z-axis. The question was to calculate $\int$B$\cdot$dl along the path PQ. I managed to get the correct answer by direct integration, ...
74 views

### How to calculate center of mass of a hollow hemi-sphere with some thickness?

When we calculate Center of mass (COM) of a hollow sphere, we assume that it's thickness is infinitesimally small, but in real world, we do not have any object with zero thickness, so how can we ...
101 views

### What is the linear momentum of a rotating body?

Let's say that a three dimensional object with continuous mass distribution is undergoing rotational motion about an axis that lies on the centre of mass. The translational velocity of the centre of ...
In the figure above, it must be noted that $R-r$ is Infinitesimal small, but it is shown bigger in the figure. here $y_{cm}$ is $y$-coordinate of center of mass (COM), $m$ is the total mass of the ...