# Integration Definition and 208 Discussions

System integration is defined in engineering as the process of bringing together the component sub-systems into one system (an aggregation of subsystems cooperating so that the system is able to deliver the overarching functionality) and ensuring that the subsystems function together as a system, and in information technology as the process of linking together different computing systems and software applications physically or functionally, to act as a coordinated whole.
The system integrator integrates discrete systems utilizing a variety of techniques such as computer networking, enterprise application integration, business process management or manual programming.System integration involves integrating existing, often disparate systems in such a way "that focuses on increasing value to the customer" (e.g., improved product quality and performance) while at the same time providing value to the company (e.g., reducing operational costs and improving response time). In the modern world connected by Internet, the role of system integration engineers is important: more and more systems are designed to connect, both within the system under construction and to systems that are already deployed.

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1. ### Calculate the electric field due to a charged disk (how to do the integration?)

I am interested in particular in the second integral, in the ##\hat{r}## direction. Here is my depiction of the problem: As far as I can tell, due to the symmetry of the problem, this integral should be zero. $$\int_0^R \frac{r^2}{(x^2+r^2)^{3/2}}dr\hat{r}$$ I don't believe I need to...
2. ### How integral and gradient cancels?

I know that gradient is multi-variable derivatives. But, here line integration (one dimensional integral) had canceled gradient. How?
3. ### How to find the constant in this indefinite integration?

$$x(t)=\int \dot{x}(t)\mathrm dt=vt+c$$ That's what I did. But, book says $$x(t)=\int \dot{x}(t)\mathrm dt=x_0+v_0 t+ \frac{F_0}{2m}t^2$$ Seems like, $$x_0 + \dfrac{a_0}{2}t^2$$ is constant. How to find constant is equal to what?
4. ### Potential energy from force

If I have a force that behaves according to the formula ##F(x)=\alpha x-\beta x^3##, how can I get the potential energy from it? I know that: $$-\frac{\mathrm{d}V(x)}{\mathrm{d}x}=F(x),$$ but what about the limits of the integration?
5. ### I Is it possible to solve such a differential equation?

Hello, I would like to is it possible to solve such a differential equation (I would like to know the z(x) function): \displaystyle{ \frac{z}{z+dz}= \frac{(x+dx)d(x+dx)}{xdx}} I separated variables z,x to integrate it some way. Then I would get this z(x) function. My idea is to find such...
6. ### Calculus and Kinematic equations---need help seeing the logic

Details of Question: ds/dt= v which becomes ds=v dt, where s=displacement, t =time, and v=velocity Then we can integrate both sides of this equation, and do a little algebra, and turn the above equation into: s − s0 = v0t + ½at2 My main question is about the integration of...
7. ### Integrating a fraction with three variables: ( sin(a) + M^2 ) / ( 1 + x^2 )

I think in the case of "n da" you can see the denominator (1+x^2) as a constant, so ∫ ( sin(a) + M^2 ) / ( 1 + x^2 ) da = ( 1 / ( 1 + x^2 ) ) * ∫ (sin(a) + M^2 ) da = ( 1 / ( 1 + x^2 ) ) * ( -cos(a) + (M^2)a ) = ( - cos(a) + (M^2)a ) / ( 1 + x^2 ) --- Is this the way to go? This is my...
8. ### Integrate ## \int \frac{zdz \cdot \hat z}{(\sqrt{p^2 + z¸^2)^3}}##

Hi, I'm trying to integrate ## \int \frac{zdz \cdot \hat z}{(\sqrt{p^2 + z¸^2)^3}}## and ## \int \frac{pdz \cdot \hat p}{(\sqrt{p^2 + z¸^2)^3}}## I get ## \frac{\hat z}{(\sqrt{p^2 + z¸^2)}}## and ## \frac{2z \cdot \hat p}{(\sqrt{p^2 + z¸^2)}}## But the correct answer should be ## \frac{z \hat...
9. ### Integration ##\ddot\phi = -\omega^2\phi##

Hi, I'm wondering how can I get ## \phi(t) = A sin(\omega t) + B cos(\omega t)## I know I have to integrate 2 times ##\ddot\phi = -\omega^2\phi##. However, I don't have any more explanation in my book. I know A and B are the constants of integration.

The Gauss-Kronrod quadrature uses the zeros of the Legendre Polynomials of degree n and the zeros of the Stieltjes polynomials of degree n+1. These zeros are the nodes for the quadrature. For example using the Gauss polynomial of degree 7, you will need the Stieltjes of degree 8 and both makes...
11. ### A Integral of 2 Bessel functions of different orders

I can only find a solution to \int_{0}^{r} \frac{1}{\rho} J_m(a\rho) J_n(b\rho) d\rho with the Lommel's integral . On my last thread (here), I got an idea about how to execute this when m = n (Bessel functions with the same order) using Lommel's integrals (Using some properties of Bessel...
12. ### Find psi(x,t) when psi(x,0)= Ae^(-x^2/a^2) and A, a are real constants

EQ 1: Ψ(x,0)= Ae-x2/a2 A. Find Ψ(x,0) So I normalized Ψ(x,0) by squaring the function, set it equal to 1 and getting an A I. A=(2/π)¼ (1/√a) B. To find Ψ(x,t) EQ:2 Ψ(x,t)= 1/(√2π) ∫ ∅(k) ei(kx-ωt)dk --------->when ω=(ħk2)/2m and integral from -∞ to +∞ EQ 3: ∅(k)= 1/(√2π) ∫ Ψ(x,0)...
13. ### Calculus What are some books for learning the techniques of Calculus?

We have so many great books available for Calculus, such as : Spivak's Calculus, Stewart Calculus, Thomas Calculus , Gilbert Strang's Calculus, Apostol's Calculus etc. These books are very nice but they teach you the concepts well and all the standard techniques that are available for solving...
14. ### 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.
15. ### 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...
16. ### 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...
17. ### 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...
18. ### 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...
19. ### 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.
20. ### 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.
21. ### 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...
22. ### 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...
23. ### Volume integral over a gradient (quantum mechanics)

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...
24. ### Attempt at volume integration to compute the full field equation

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...
25. ### Using Trig Substitution in Trig Integration

Homework Statement Integrate: $$\int \frac{dx}{x^2\sqrt{4-x^2}}dx$$ Homework Equations 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...
26. ### I What is the integral of energy?

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...
27. ### How to solve this differential equation?

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 equation...
28. ### Integration of an analytical expression

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.
29. ### Cylindrical Coordinates: Line Integral Of Electrostatic Field

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}##...
30. ### I Integrating a differential

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?
31. ### Definite Integral of Product/Composite Function Given Graph

Homework Statement Given the graph of f(x) shown below, find the value of the integral. Photo attached. Homework Equations [/B] ∫23 5x·f(x2)dx The Attempt at a Solution [/B] I tried integration by parts to simplify the problem, but finding the integral of the composite function (f(x2))...
32. ### Help finding ths Fourier transform

Homework Statement find the fourier transform of the following function in two ways , once using direct computation , and second using the convolution therom . Homework Equations Acos(w0t)/(d2+t2) The Attempt at a Solution I tried first to solve directly . used Euler's identity and got...
33. ### B Kinematics in calculus

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...
34. ### Integration help on physics problem

Homework Statement Homework Equations F=ma F/m = a The Attempt at a Solution Fc = constant force fquad= cv'^2 [/B] (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)) dv' dt'...
35. ### I Integrating unit vector ρ

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
36. ### I Discrete integration

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...

40. ### A simple case of translation invariance of Riemann integrals

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. Homework Equations Normally we find Riemann integrals by creating a rectangle R that includes A and set the function to be zero when x...
41. ### Order of multi-variable integration of infinite range

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 Homework Equations The Attempt at a Solution Then, the...
42. ### Integration over a ball

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). Homework Equations 3. The Attempt at a Solution [/B]...
43. ### 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...
44. ### Deflection of Tapered Beam with Elliptic Cross Section

I am working on deriving expression for deflection of a tapered beam with an elliptic cross-section. Hence, area moment of inertia is a linear function of the beam length. The beam is fixed at one end, and a concentrated force F is applied on its tip at the free end. I am using the known...
45. ### What does the area under a volume vs time graph represent?

Homework Statement I have a function showing the volume of water in a bay at different times in the day, and I want to know what the area under this curve would represent (if it represents anything meaningful). I know how to integrate, so that isn't a problem. Homework Equations I am...
46. ### Calculation of flux

Homework Statement A ##10 cm## (on y axis) by ##10 cm## (on z axis) flat plate is located ##5 cm## away (on x axis) from a point charge ##q##. Calculate the electric flux from the point charge to the plate. Can somebody solve it using surface integral using both spherical and cartesian...
47. ### Integral sqrt((5-x)/x)

Homework Statement integration with respect to x Homework Equations integral 1/sqrt (a^2 - x^2) = arcsin(x/a) The Attempt at a Solution image attached, the arcsine term in 5/2 arcsin((2x-5)/5) it should be 5 arcsine(sqrt(x/5))
48. ### Integration of an interaction force to find potential energy

Homework Statement A particle that can move along the x-axis experiences an interaction force Fx=(3x2−5x) N where x is in m. Find an expression for the system's potential energy. Express your answer in terms of the variables x and the constant of integration C, where C is in joules. Homework...
49. ### Simple integration to find area

Homework Statement I wish to find the area under the curve y = 1/2^x between x=0 and x=1 but get an answer that is half the expected answer. Homework Equations Integrate y = 1/2^x to get -1/(2^x ln2) + Const This integration result was confirmed on Wolfram Slot in the range x = 0 to x = 1...
50. ### Converting Simulink model to C code, integration

Dear Forumers, Given a simulink model: http://www.femm.info/Archives/contrib/images/TransientLoudspeaker/SimulinkOverview.png I would like to implement fast code for it. I have no access to matlib or simulink at all, so I tried to implement the simulation in C code. Code for the block...