integration

1. A Challenging Integral

Homework Statement: The question is in Attempt at a solution. Homework Equations: x=tanA/b I tried by substituting x=tanA/b but it did'nt helped.Now I cannot think of any other thing to do.Help.
2. A Does this integration have a closed form solution?

I was trying to solve a differential equation that I defined to study the dynamics of a system. Meanwhile, I encounter integration. The integration is shown in the image below. I tried some solutions but I am failed to get a solution. In one solution, I took "x" common from the denominator terms...
3. Calculating Divergent Amplitude in Phi-4 Theory

For the diagram In scalar field theory, I have obtained an integral which looks like $$\int_{0}^{\Lambda} \frac{d^4 q}{(2\pi)^4} \frac{i}{q^2 - m^2 + i\varepsilon} \frac{i}{(p - q)^2 - m^2 + i\varepsilon}$$ I am required to calculate this and obtain the divergent amplitude...
4. I Website for integration?

I remember being given a ghastly book of integrals to learn when I was about 16. I went to sleep. Apparently the first book of integrals was published by Meier Hirsch in 1810. There have been many more since then. Surely with the invention of the internet there is something better? Symbolab has...
5. I Calculus- Area between two curves (minimize it)

Hi, This is my first question here, so please apologise me if something is amiss. I have two curves such that Wa = f(k,Ea,dxa) and Wb = f(k,Eb,dxb). I need to minimize the area between these two curves in terms of Eb in the bounded limit of k=0 and k=pi/dx. So to say, all the variables can...
6. B What region in NMR spectrum should I choose for integration?

Hi all, I have nuclear magnetic resonance spectrum. The vertical axis is intensity, and the horizontal axis is index. I need to find integral under the peak. But I am not sure, what region should I choose for integration - region 1 or region 2? Please find attached the spectrum.
7. Potential energy of a shell and a disc, both covered uniformly with charge

Double integration maybe?? I calculated potential due to shell on plate's center but not on other points on it's surface.
8. A Ideas for determining the volume of a rotating object

Hello everybody, I am currently working on an experiment investigating the formation of planets. I have a vacuum chamber in which dust particles form bigger agglomerates through accretion (sticking together). From the imagery I can see those agglomerates which are build up by smaller...
9. Hemisphere pump problem

<Moderator's note: Moved from a technical forum and thus no template.> > The tank (hemisphere) is full of water. Using the fact that the weight of water is 62.4 lb/ft3, find the work required to pump the water out of the outlet. The radius of the hemisphere is 10. $V =\pi x^2 h$ using the...

27. A simple case of translation invariance of Riemann integrals

1. Homework Statement Show that \int_{A} 1 = \int_{T(A)} 1 given A is an arbitrary region in R^n (not necessarily a rectangle) and T is a translation in R^n. 2. Homework Equations Normally we find Riemann integrals by creating a rectangle R that includes A and set the function to be zero...
28. Order of multi-variable integration of infinite range

1. Homework Statement If the Green's function of the electric field in a system is G(x,x')=e^{-i(x-x')^2} I want to calculate the phase of the electric field at x if the source is uniformly distributed at x'=-\infty to x'=\infty 2. Homework Equations 3. The Attempt at a Solution...
29. Integration over a ball

1. Homework Statement I'm working on a generalization of gravitation to n dimensions. I'm trying to compute gravitational attraction experienced by a point mass y due to a uniform mass distribution throughout a ball of radius a -- B(0, a). 2. Homework Equations 3. The Attempt at a Solution...
30. Integration Question Help

1. The problem statement, all given data I've been working through one of the lessons for my HNC and I'm totally stuck on how they got from 27.84x10^-6 to 3.593x10^4. I can follow it all fine including the integration after that section it's just the inbetween that I can't seem to get my head...