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.
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...
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...
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...
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...
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.
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...
<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...
1. Homework Statement
1) Calculate the density of states for a free particle in a three dimensional box of linear size L.
2) Show that ##\int f \nabla g \, d^3 x=-\int g \nabla f \, d^3 x## provided that ##lim_{r \rightarrow \inf} [f(x)g(x)]=0##
3) Calculate the integral ##\int...
I'm trying to figure out this volume integral, a triple integral, of a 9-variable function.
3 Cartesian-dimension variables, and 6 primed and un-primed co-ordinates.
After the volume integration, the un-primed co-ordinates will have been gotten rid of, leaving a field function in terms of...
1. Homework Statement
Integrate: $$\int \frac{dx}{x^2\sqrt{4-x^2}}dx$$
2. Homework Equations
3. The Attempt at a Solution
I got to the final solution ##\int \frac{dx}{x^2\sqrt{4-x^2}}dx=-\frac{1}{4}cot(arcsin(\frac{1}{2}x))##. But It's the method where you transform that to the solution...
So the classical law of force given by Newton is F= ma = dp/dt = qE. Thus if i integrate the last two equivalents I get:
∫(dp/dt)dt = q∫Edt
p + C = q∫Edt
correct?
then what would the integral of...
1. Homework Statement
We solved the differential equation (2.29), , for the velocity of an object falling through air, by inspection---a most respectable way of solving differential equations. Nevertheless, one would sometimes like a more systematic method, and here is one. Rewrite the...
I have an equation regarding integration equation. Given:
where is found analytically to be:
My question is what is the analytical equation for equation 3? I hope that anyone may help me regarding this matter. This is the paper I referred: https://arxiv.org/pdf/1503.05793.pdf
Thank you.
1. Homework Statement
An electrostatic field ## \mathbf{E}## in a particular region is expressed in cylindrical coordinates ## ( r, \theta, z)## as
$$ \mathbf{E} = \frac{\sin{\theta}}{r^{2}} \mathbf{e}_{r} - \frac{\cos{\theta}}{r^{2}} \mathbf{e}_{\theta} $$
Where ##\mathbf{e}_{r}##...
Let's say we have ##df=2xy^3dx + 3x^2y^2dy## - this is an exact differential.
In integrating, to find f, can we write ## f = \int 2xy^3 \, dx + \int 3x^2y^2 \, dy = 2x^2y^3 + C ##
Or am I getting it wrong?
1. Homework Statement
Given the graph of f(x) shown below, find the value of the integral.
Photo attached.
2. Homework Equations
∫23 5x·f(x2)dx
3. The Attempt at a Solution
I tried integration by parts to simplify the problem, but finding the integral of the composite function (f(x2))...
1. Homework Statement
find the fourier transform of the following function in two ways , once using direct computation , and second using the convolution therom .
2. Homework Equations
Acos(w0t)/(d2+t2)
3. The Attempt at a Solution
I tried first to solve directly . used Euler's identity and...
hi, i'm a high-school student that is just beginning to learn calculus.
in calculus we are learning how to apply integration and diffrentiaiton methods regarding kinematics.
there is this certain phrase i do not really understand in our textbook: e.g."in the second second"
how am i meant to...
1. Homework Statement
2. Homework Equations
F=ma
F/m = a
3. The Attempt at a Solution
Fc = constant force
fquad= cv'^2
(Fc-cv'^2)/m = a
(Fc-cv'^2)/m = dv' / dt' * using the primes to differentiate between v and v' during integration
dt '(Fc-cv'^2) dv'*(m)
dt' = (m/ (Fc-cv'^2))...
When doing integration such as \int_{0}^{2\pi} \hat{\rho} d\phi which would give us 2\pi \hat{\rho} , must we decompose \hat{ρ} into sin(\phi) \hat{i} + cos(\phi) \hat{j} , then \int_{0}^{2\pi} (sin(\phi) \hat{i} + cos(\phi)\hat{j}) d\phi , which would give us 0 instead?
Thanks
I have values for the variables (C, v, g, w at all sample points) but I do not know how to evaluate the integral. This equation is supposed to be implemented on a computer as part of a larger algorithm for navigation purposes. I have a feeling that the gyroscope sensor reading and or the...
1. Homework Statement
Real atomic nuclei are not point charges, but can be approximated as a spherical distribution with radius ##R##, giving the potential
$$ \phi(r) = \begin{cases}
\frac{Ze}{R}(\frac{3}{2}-\frac{1}{2}\frac{r^2}{R^2}) &\quad r<R\\
\frac{Ze}{r} &\quad r>R \\...
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...
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...
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...
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...