What is Integration: Definition and 1000 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. E

    B Confused about holding variables constant during integration

    For a double integral, we might treat the "inner integral" separately and be able to compute something like ##\int_{x_1}^{x_2} f(x,y) dx## by holding ##y## constant during the integration. The same technique is applied in other places too, like for solving exact differential equations. I haven't...
  2. LCSphysicist

    I Integrate 1/(x*lnx): Integration by Parts

    can integrate 1/(x*lnx) by parts??
  3. S

    MHB Understanding Example from Topics in Banach Space Integration

    Hey Could you give me a hint how to explain this example? Need help to prove statement in red frame. Example from book (Topics In Banach Space Integration) by Ye Guoju‏، Schwabik StefanThank you
  4. T

    I Surface of a cone by integration

    If i want to calculate the volume of a cone i can integrate infinitesimal disks on the height h of the cone. I was told that if i want to calculate the surface of the cone, this approximation is not correct and i have to take the slanting into account, this means that instead of...
  5. C

    Can indefinite integration be simplified using substitution?

    Let x=t^2 Then dx=2t dt Integral of 1/(x(1-x))^(1/2)dx = integral of 2tdt/t(1-t^2) ^(1/2) = integral of 2dt/(1-t^2) ^(1/2) = 2 arcsin(t) +c = 2 arcsin(rt(x)) +c. But the answer in my book is arcsin(2x-1) +c. Tell me how 2 arcsin(rt(x) +C= arcsin(2x-1) +c I know the constant will vary for both...
  6. Vick

    I How to Calculate Weights for Gauss-Kronrod Quadrature Using Nodes and Degree?

    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...
  7. Sokolov

    Integration of inexact differentials in Thermodynamics

    In Thermodynamics, I have seen that some equations are expressed in terms of inexact differentials, ##\delta##, instead of ##d##. I understand that this concept is introduced to point out that these differential forms are path-dependent, although I am not clear how they can be handled. So, are...
  8. S

    Integration of an exponential and algebra

    ##\int \frac{e^x (2-x^2)}{(1-x) \sqrt{1-x^2}} dx## I tried using substitution x = sin θ but still can not solve it. I guess I have to get rid the term ex but do not know how Thanks
  9. J

    MHB Value of k in definite Integration

    Let p(x)=2x^6+4x^5+3x^4+5x^3+3x^2+4x+2. Let \displaystyle I_{k}=\int^{\infty}_{0}\frac{x^k}{p(x)}dx where 0<k<5. Then value of k for which \displaystyle I_{k} is smallest.
  10. penroseandpaper

    I Integration of a hyperbolic function

    The integral of cothx is ln|sinhx|+C. Does this mean the integral of coth2x is ln|sinh2x|+C? If not, does anyone have a link to a page on how it is achieved - I'm trying to compile a list of all common hyperbolic function derivatives and integrals. However, I can't find anything to confirm if...
  11. A

    Integration in polar coordinates

    In spherical poler coordinates the volume integral over a sphere of radius R of $$\int^R_0\vec \nabla•\frac{\hat r}{r^2}dv=\int_{surface}\frac{\hat r}{r^2}•\vec ds$$ $$=4\pi=4\pi\int_{-\inf}^{inf}\delta(r)dr$$ How can it be extended to get $$\vec \nabla•\frac{\hat r}{r^2}=4\pi\delta^3(r)??$$
  12. Math Amateur

    I Riemann Integration ... Existence Result .... Browder, Theorem 5.12 ....

    I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 5: The Riemann Integral and am currently focused on Section 5.2 Existence Results ... ... I need some help in understanding the proof of Theorem 5.12 ...Theorem 5.12 and its...
  13. Math Amateur

    MHB Riemann Integration ... Existence Result .... Browder, Theorem 5.12 ....

    I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 5: The Riemann Integral and am currently focused on Section 5.2 Existence Results ... ... I need some help in understanding the proof of Theorem 5.12 ...Theorem 5.12 and its...
  14. tworitdash

    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...
  15. T

    Help with this Integration please

    Summary:: I just need to know how we got from the 'beginning point' to the 'end point'/'answer'. The left side is where we start and my professor did a bunch of calculations so fast that I wasn't able to understand how he got the result on the right side. Could someone help me integrate this...
  16. tworitdash

    A Integration of Bessel's functions

    I can only find a solution to \int_{0}^{r} \rho J_m(a\rho) J_n(b\rho) d\rho with the Lommel's integral . The closed form solution to \int_{0}^{r}\frac{1}{\rho} J_m(a\rho) J_n(b\rho) d\rho I am not able to find anywhere. Is there any way in which I can approach this problem from scratch...
  17. V

    Finding volume using integration

    I know that the formula for volume is equal to the definite integral ∫A(x)dx, where A(x) is the cross sectional. I found the definite integral where b=5 and a=0, for ∫4x2dx. I obtained the answer 500/3, however this was incorrect, and I'm unsure of where I went wrong? Thank you.
  18. jk22

    I Integration : Are a function and it's derivative independent?

    The question is a bit confused, but it refers to if the following integration is correct : $$I=\int \frac{1}{1+f'(x)}f'(x)dx$$ $$df=f'(x)dx$$ $$\Rightarrow I=\int\frac{1}{1+f'}df=?\frac{f}{1+f'}+C$$ The last equality would come if I suppose $f,f'$ are independent variables.
  19. M

    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)...
  20. karush

    MHB 4.2.8 AP calculus Exam Integration limits

    ok I posted a image to avoid any typos but was wondering why the question has dx and options are in dt I picked C from observation but again that was assuming f was a horizontal line of which it could be something else that way the limits stay the same but the area is cut in halfopinions...
  21. jisbon

    Understanding Integration by Substitution

    Not sure how do I start from here, but do I let $$u = lnx$$ and substitute? Cheers
  22. Adesh

    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...
  23. C

    A change in the order of integration

  24. Physics lover

    Challenging Integral Homework: Attempting x=tanA/b Substitution

    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.
  25. anita chandra

    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...
  26. D

    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 $$i\mathcal{M} =...
  27. Z

    Integration limitations to a SiC microprocessor

    There has been a demonstration of SiC BJT ADCs, and SiC JFET SRAM. What would be the major limitations associated with higher forms of integration for SiC? For example, a 1billion transistor CPU based on SiC?
  28. E

    Definite and indefinite integration in the definition of work

    This is going to sound like a silly question, but here we go anyway! I've always thought about a definite integral being used for modelling a change in some quantity whilst an indefinite integral is employed to find the defining function of that quantity. For example, consider the...
  29. George Keeling

    I Is There a Better Way to Solve Integrals Than Symbolab and Mathematica?

    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...
  30. B

    I Integration: When to multiply by one or add zero?

    I have seen several functions be integrated by multiplying by a form of one or by adding a form of zero. When is it advantageous do do one of these things? Are there any example problems (Calc I or II) in which I can try these techniques?
  31. G

    How to use the Double integration method for an overhanging beam?

    In case of overhanging beam with point load at the end. For example: (here RA-reaction is negative) The equation will be as follows (by double integration method): , as we can see the equation will not have Point load (10kN) term in it. 1) How the influence of the point load is accounted in...
  32. mastrofoffi

    I Integration of Poisson's Equation

    I have a gaussian charge distribution, in gaussian units $$ \rho(\mathbf r) = q\frac{\alpha^3}{\pi^{3/2}}\exp( -\alpha^2 r^2 ) $$ and I want to solve Poisson's equation to find the electrostatic potential $$ \nabla^2 \psi(\mathbf r) = -4\pi\rho(\mathbf r). $$ Since the charge distribution has...
  33. archaic

    B Interpreting integration otherwise

    There's one odd way to think about integration when it comes to interpreting it as a sum. suppose for a second that ##x## is in meters, you could think of distance as an infinite number ##n## of "points" in space, ##n→∞##, then in this case ##f(x)Δx## would mean that you now have ##nf(x)##...
  34. S

    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...
  35. C

    Differential Integration Problem

    Attempt at solution: Writing the chain rule for ## E(V,T) ##: ## dE = \frac{\partial E}{\partial T}dT + \frac{\partial E}{\partial V}dV ## Then, integrating the differential: ## \int{ dE } = \int{ \frac{\partial E}{\partial T}dT } + \int{ \frac{\partial E}{\partial V}dV } ## If I put the...
  36. T

    Help with a complex integration in QFT

    N/A
  37. snatchingthepi

    Help please in understanding the limits of this integration

    So I can push this integral all the way to the end and see I get a negative volume. I solve for the intercepts of the cone and sphere at r^2 = 1/2. Seeing this cone is inside the sphere and the sphere is around it, I figure I should integrate from sqrt(1/2) to 1 since we're dealing with a unit...
  38. C

    Calculating Integrals Using the Fundamental Theorem of Calculus

    Here, width of first bar, y=x^2=a^2 y=x^2=(a+Δx)^2 height of nth bar=y=(a+(N-1)Δx)^2 Total area,I={a^2+(a+Δx)^2+(a+2Δx^2)+...+[a+(N-1)Δx]^2}Δx I={Na^2 + 2aΔx +...} I can't seem to get forward to get the required result which is 1/3(b^3-a^3)
  39. N

    How to combine integration equation in Python?

    I'm calculating key rate (R^Rate-wise) by integrating R(eta) over all possible eta from 0 to 1, with a probability distribution (PDTC) which is a log-normal distribution. The equation of log-normal distribution: The equation of R(eta): Therefore, R^Rate-wise =...
  40. L

    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.
  41. Dr-LucienSanchez

    Calculate the total resistance by integration using the conductivity equation

    (i) Dividing the rod into thicknesses of dx we get discs of area A with lengths=dx so using (****) we have the resistance of a typical disc (between point x' and x'+dx) as: (1) ##R(x'dx)=\frac{dx}{g(x)A}## (ii) Using (1) and (*) and the integrating from a to b of the entire rod we get...
  42. amjad-sh

    How Do You Integrate sin(2kz) from Negative Infinity to z?

    ##\int_{-\infty}^{z}sin(2kz)\,dz=\dfrac{-1}{2k} \Big [cos(2kz) \Big ]_{-\infty}^z=-\dfrac{cos(2kz)}{2k}+\dfrac{cos(-\infty)}{2k}##. I ended up here, and I don't know how to proceed. One recommended me to use contour integration, but I have no idea about it.
  43. J

    MHB Integration in Polar Coordinates (Fubini/Tonelli)

    Let $S^{n-1} = \left\{ x \in R^2 : \left| x \right| = 1 \right\}$ and for any Borel set $E \in S^{n-1}$ set $E* = \left\{ r \theta : 0 < r < 1, \theta \in E \right\}$. Define the measure $\sigma$ on $S^{n-1}$ by $\sigma(E) = n \left| E* \right|$. With this definition the surface area...
  44. Y

    Correcting Integration of tan^5x: Differentiating and Verifying the Solution

    This is my working out, and I also included the correct answer in the last line. The answer used a different method, however, what did I do wrong with my method? Thanks for the help!
  45. Gursimran Singh

    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.
  46. Lardos

    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...
  47. M

    An integration problem using trigonometric substitution

    This is the integral I try to take. ##\int\sqrt{1+9y^2}## and ##9y^2=tan^2\theta## so the integral becomes ##\int\sqrt{1+tan^2\theta}=\sqrt {sec^2\theta}##. Now I willl calculate dy. ## tan\theta=3y ## and ##y=\frac {tan\theta}3## and ##dy=\frac{1+tan^2\theta}3## Here is where I can only...
  48. JD_PM

    What are the limits of integration for this surface integral?

    I want to compute: $$\oint_{c} F \cdot dr$$ I have done the following: $$\iint_{R} (\nabla \times v) \cdot n \frac{dxdy}{|n \cdot k|} = \iint (9z-1) dxdy$$ I don't know what limits the surface integral will have. Actually, I am not sure what's the surface. May you shed some light...
  49. J

    Integration of traceless symmetric matrices

    Hi, I stumbled upon an identity when studying tensor perturbations in cosmology. The formula states that $$ \int d^2\hat{p} f(\hat{p}.\hat{q})\hat{p}_i \hat{p}_k e_{jk}(\hat{q}) = e_{ij}(\hat{q})/2 \int d^2\hat{p} f(\hat{p}.\hat{q})(1-(\hat{p}.\hat{q})^2), $$ where ##e_{ij}## is a symmetric...
  50. looseleaf

    A Understanding Integration by Parts in Quantum Field Theory

    Hello, I'm just starting Zee's QFT in a Nutshell, I'm a bit confused about what he means by "integate by parts under the d4x". Can someone explain what he means by this? I understand how to obtain the Klein-Gordon equation from the free particle Lagrangian density, but not sure why he invokes...
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