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. J

    MHB Differentiation / Integration Help

    The curve has a gradient function dy/dx = 2 +q/(5x^2) where q is a constant, and a turning point at (0.5, -4). Find the value of q. option 1 : 2.5 option 2: -2.5 option 3: 0 Option 4: -3 I couldn't find the answer and will need assistance to how the answer can be obtained. I have...
  2. M

    Change integration limits for cylindrical to cartesian coord

    Homework Statement I want to change the integration limits of an integral in cylindrical to cartesian coordinates. For example the integral of function f(r) evaluated between b and R: ∫ f(r)dr for r=b and r=R (there is no angular dependence). For write de function in cartesian coordinates...
  3. C

    Python Numerical integration 'quad' error

    I have defined a series of functions below with the end function `fA` being inserted for a numerical integration. The integration is with respect with one variable so the other arguments are passed as numeric so that the integration method (quad) may proceed import numpy import...
  4. alijan kk

    Leibniz Integral Rule Explained

    1. The problem statement, a ll variables and given/known data Homework Equations The Attempt at a Solution what is t equal to here , how should i think it ?
  5. W

    Vector Integration: Fundamental theorem use

    Homework Statement Could someone illustrate why $$\int_{V} \nabla \cdot (f\vec{A}) \ dv = \int_{V} f( \nabla \cdot \vec{A} ) \ dv + \int_{V} \vec{A} \cdot (\nabla f ) \ dv = \oint f\vec{A} \cdot \ d\vec{a}$$ ? Homework EquationsThe Attempt at a Solution I understand that the integrand can...
  6. F

    Calculate Electric Flux from Point Charge to Plate:

    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...
  7. chwala

    Find f'(x): f'(x) = ##\frac {dy} {dx},\frac {dx}{dt}= \frac {8t^7}{1+t^{16}} ##

    Homework Statement if ## f(x)= \int_x^3 \sqrt {1+t^{16}} dt ## find f'(x)Homework EquationsThe Attempt at a Solution let ## x = 1+t^{16},## → ##\frac {dx}{dt},= 16t^{15},## ## y= x^{1/2} ## →##\frac {dy} {dx},= 0.5x^{-0.5}##
  8. M

    MATLAB Numerical Integration with variable limits MATLAB

    Hi PF! Suppose I have two functions ##f(x),\,g(y)## that are numerically defined as vectors (i.e. ##g(y) = [0,1,4,9,16]:y = [0,1,2,3,4]## and say ##f(x) = [0,1,8,27,64]:x = [0,1,2,3,4]##) and am trying to compute $$\int_0^1 f(x) \int_x^1 g(y)\, dydx.$$ How would I do this in MATLAB? I could be...
  9. Peter Alexander

    Understanding the Cauchy Integration Formula for Analytic Functions

    Hello everyone! I'm having a bit of a problem with comprehension of the Cauchy integration formula. I might be missing some key know-how, so I'm asking for any sort of help and/or guideline on how to tackle similar problems. I thank anyone willing to take a look at my post! Homework Statement...
  10. J

    Double Integration Homework: Changing Limits

    Homework Statement Homework Equations I've drawn graph below. The Attempt at a Solution Currently their limits are y = 0 to y = x - 2 vertical arrow and x = 2 to x = infinite. horizontal arrow Changing limits i get right side graph. x = y + 2 to x = infinite horizontal arrow y = 0 to y =...
  11. C

    Solving Contour Integration Homework

    Homework Statement For R > 0, assume ΓR is a circle {z ∈ C : |z| = R} with anticlockwise direction. For which R>0, does the the function f(z) = 1/sin^(2)(z) be continuous on ΓR and evaluate ∫_{ΓR} dz/sin^(2)(z) for each R (the answer may be dependent on R). Homework Equations sinx= (e^(ix)...
  12. V

    Integration with Respect to x: Integral of 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))
  13. R

    Easy matrix integration question

    Homework Statement This is just the triple integral of an easy matrix problem. I just have no ideas what they got by the time they got to the integral of x. Homework Equations integral[/B]The Attempt at a Solution Somebody please prove me wrong. I got a matrix of constants by the time I got...
  14. T

    I Integration above or below axis

    If you are trying to find the integral of a function with a complex pole on the real axis (i.e. ##[-\infty,\infty]##) via analytic continuation, does it matter if you integrate along a contour either in the upper-half plane or lower-half plane? I was under the assumption that either approach was...
  15. R

    I Solving Integration by Parts for Relativistic Kinetic Energy

    Hi, I've been following a derivation of relativistic kinetic energy. I've seen other ways to get the end result but I'm interested in finding out where I've gone wrong here: I'm struggling with integrating by parts. The author goes from...
  16. S

    Solve Tricky Integration: ##\frac{20\ln{(t)}}{t}##

    Homework Statement How do I solve ##\frac{20\ln{(t)}}{t}##? Homework EquationsThe Attempt at a Solution Is it easier to calculate this without integrating by parts? I'm not sure where to start.
  17. C

    How to Convert Rectangular Integrals to Polar Coordinates Correctly?

    Homework Statement Trying to help a friend with a problem. We are supposed to solve the below using polar coordinates. The actual answer is supposed to be π/16. Solving the integral is not the issue, just converting it. 2. The attempt at a solution What I got sort of worked, but it is only...
  18. EastWindBreaks

    I dont understand this integration

    Homework Statement in the textbook, it says: how does the integral of y'' gives you y' like that? Homework Equations given C_a is a dimensionless peak acceleration factor. The Attempt at a Solution [/B]
  19. I

    I Dirac-Delta Function, Different Integration Variable

    Hello, I know that the derivative of Dirac-delta function (##\delta'(x-x') = \frac{d}{dx} (\delta(x-x')))## does the following: ##\int_{-\infty}^{\infty}\psi(x')*\delta'(x-x') dx' = \frac{d\psi(x)}{dx}## it is easy to visualize how the delta function and the function ##\psi(x')## interact along...
  20. M

    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...
  21. Lazy Rat

    Integration of an equation relating to electrostatics

    Homework Statement Hi I was wondering if anyone could give me a hand with this problem I'm trying to solve. I am trying to integrate this equation twice. I'm not really sure what to do with the right hand side of the equation.Homework Equations The Attempt at a Solution [/B] The left side...
  22. yeshuamo

    Variable of integration in geometric phase calculation

    Homework Statement Calculate the geometric phase change when the infinite square well expands adiabatically from width w1 to w2.Homework Equations Geometric phase: \gamma_n(t) = i \int_{R_i}^{R_f} \Bigg< \psi_n \Bigg | \frac{\partial \psi_n}{\partial R} \Bigg > dR Infinite square well wave...
  23. Z

    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...
  24. P

    I Numerical Integration twice (acceleration to displacement)

    Hello everyone I have the following question regarding numerical integration twice from acceleration to displacement. Suppose that a particle has acceleration function of a = tt (which has non-elementary integral), to find the velocity it is easy as I can use Simpson's rule for numerical...
  25. V

    Can you handle this integration with limits problem?

    Homework Statement Integrate ∫ (tan √x) / (2 √x) dx Homework Equations Limits from 0 to ∞ The Attempt at a Solution Put u = √x du/dx = 1/ (2 √x) dx = du * (2 √x) now question becomes ∫ tan u du = log sec u = log (sec √x) now applying limits ∫ tan u du = log (sec √∞) - log (sec √0) = log...
  26. Q

    Help with bounds for integration

    Homework Statement I'm trying to change the bounds for this integral Sin(x^2)dxdy With x going from 1 to 2y, y going from 0 to 1 (I already know the integration for sin(x^2) The Attempt at a Solution I converted 2y=x to 1/2x=y and graphed all the bounds. I went with 1,2 for my...
  27. yecko

    Triple integration - find volume

    Homework Statement Homework Equations in the pic The Attempt at a Solution why is there an extra "r" in the highlighted line? my attempt: ## \int_0^{2\pi}\int_0^2\int_{r^2}^41\ dy\ r\ dr\ d\theta ## = ##\int_0^{2\pi}\int_0^2\left(4-r^2\right)\ r\ dr\ d\theta## thanks
  28. L

    Finding the Expression for v Using Partial Integration

    Homework Statement For an analytic function, f(x+iy)=u(x,y)+iv(x,y),u is given by u=(3x^2) -(3y^2). The expression for v, considering K to be a constant is? Homework Equations δu/δx=δv/δy δu/δy=-δv/δx [/B] The Attempt at a Solution My attempt :- u=(3x^2) -(3y^2) δu/δx=6x &...
  29. S

    Can Wolfram Mathematica be wrong on this Integration?

    Homework Statement Mathematica vs (Symbolab + my brain) Homework EquationsThe Attempt at a Solution I think this integral calculation in Mathematica is wrong. Open pictures below. Please help me. Graphs (the red one is under the blue and the green): https://ibb.co/bACa3G Wolfram Mathematica...
  30. Alexanddros81

    Simple Pendulum motion - Numerical Integration

    Homework Statement The differential equation of motion for the simple pendulum can be shown to be ##\ddot {θ} = -(g/L)sinθ##. Given that L=9.81 m and that the pendulum is released from rest at θ=60deg, determine the time required for the pendulum to reach the position θ=0deg. Use Δt=0.10s, and...
  31. L

    Integration of even powers of sine and cosine

    Homework Statement Homework Equations cos2x = (1+cos2x)/2 sin2x = (1-cos2x)/2 The Attempt at a Solution I believe you would use the double angle formula repeatedly but that is very tedious; is there a more concise way to solve the problem?
  32. F

    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...
  33. S

    I Integration of a one form

    Hello! In Nakahara's Geometry, Topology and Physics in chapter 6.4.5 second edition, he proves at a point that on a simply connected manifold, the first de Rham cohomology group is trivial. In the proof he defines ##\alpha : I=[0,1] \to M##, homotopic to a point. Now, by the rules of integration...
  34. N

    Integration by parts/substitution

    Hi. I think I jumped too eagerly into my latest module, as I am positive it makes many assumptions on previous experience. I am obviously lacking. I have created a question in Word, but the equations don;t appear to be copying into this thread. So I have uploaded question instead. If this is...
  35. Q

    Triple Integration: Solve Homework Equation

    Homework Statement I'm trying to figure out the other parameters to solve the problem Homework Equations I know sqrt(x^2+y^2+z^2) = p The Attempt at a Solution I changed the integrand to p^3 sin(theta) since p * p^2 sin(theta) Then for the first integration sign, I know how to get the...
  36. Math Amateur

    MHB Complex Integration - Conway - First Example on page 63 .... Section 1, Ch. IV .... ....

    I am reading John B. Conway's book, "Functions of a Complex Variable I" (Second Edition) ... I am currently focussed on Chapter IV: Complex Integration ... Section 1: Riemann-Stieljes Integral ... ... I need help in fully understanding the first example on page 63 ... ... The the first...
  37. W

    Contour Integration: Branch cuts

    Homework Statement I am supposed to evaluate the contour integral of the positive branch of ##z^{-1/2}## over the following contour: I believe the answer should be 0, by Cauchy's theorem (loop encloses no poles), but my methods of parameterization have led to non-zero answers. Homework...
  38. M

    I Three different integration schemes

    I'm solving a first order linear ODE system numerically three different ways: implicit Euler, explicit Euler, and RK4. Attached are the plots of the numerical solutions (line and stream of small closely-connected dots) and the exact solution (big dots). Also I plot the maximum error (right...
  39. C

    Finding torque by integration of weight

    Homework Statement Hi. I ve got a problem, where I have to show torque by integrating the weight of the rod over the whole it's length. Homework Equations [/B] Result, what I am suppose to get is: ## \tau_{rod} = \frac{mgb}2 ##The Attempt at a Solution [/B] When I try to integrate, I am...
  40. S

    Error of integration in numerical methods

    Homework Statement So this is a problem for my numerical methods class. We are doing integration and derivation. The part that I am stuck on is why does the midpoint method and trapezoidal method both have error of order ##h^2##, when the first one is one point integration method while the...
  41. R

    Integrating Multiple Solid Volumes: xy-Plane, x=1, x=3

    Homework Statement A solid is bounded by the surface z=x^2-y^2, the xy-plane, and the plane x=1 and x=3. Compute, by double integration, the volume of the the solid. Homework EquationsThe Attempt at a Solution I know that the height is the z function and the lower limit of is x= 1 and upper...
  42. Moayd Shagaf

    Calculus A Book on Methods of Integration

    Is there a book that can teach me every single method of integration (except Ryzhik) and Special Functions (Bessel,Hermite,Legendre ,Spherical Harmonics). since I'll be use it in QFT ,It will be very useful to have strong in Bessel Functions and Others Functions and Integrals.
  43. J

    'Unusual' mathematical step in integration

    I'm following a derivation in my lecture notes of total average particle number in an ideal classical gas (statistical physics approach). I follow it to the line (though the specific terms don't matter): \left<N\right> = e^{\mu/\tau} \frac{\pi}{2} \int_0^\infty \left(n \,dn \,e^{- \frac{\hbar^2...
  44. L

    A Integration along a loop in the base space of U(1) bundles

    Let ##P## be a ##U(1)## principal bundle over base space ##M##. In physics there are phenomenons related to a loop integration in ##M##, such as the Berry's phase ##\gamma = \oint_C A ## where ##C(t)## is a loop in ##M##, and ##A## is the gauge potential (pull back of connection one-form of...
  45. B

    Normalization of Wavefunction Integration

    Homework Statement [/B] Determine the value that A (assumed real) must have if the wavefunction is to be correctly normalised, i.e. the volume integral of |Ψ|2 over all space is equal to unity. Homework Equations Integration by parts (I think?) The Attempt at a Solution So, I've managed...
  46. Math Amateur

    MHB Riemann Integration - The Additivity Theorem .... B&S Theorem 7.2.9 ....

    I am reading "Introduction to Real Analysis" (Fourth Edition) by Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 7: The Riemann Integral ... I need help in fully understanding an aspect of the proof of Theorem 7.2.9 ...Theorem 7.2.9 and its proof ... ... read as follows...
  47. S

    I Is there any good book to easy to self learn Integration?

    I have learned differentiation (till multiple order differentiation). But I don't just understand integrals.
  48. Delta31415

    Calculus Integration help please -- involves sinh(x), e^x and roots

    Homework Statement [/B] $$\int \left ( \frac{-1}{2*\sinh(x)*\sqrt{1-e^{2x}})} \right ) dx$$ or http://www.HostMath.com/Show.aspx?Code=\int \left ( \frac{-1}{2*\sinh(x)*\sqrt{1-e^{2x}})} \right ) dx Homework Equations the sinh identity, which is (e^x-e^-x)/2 The Attempt at a Solution Tried...
  49. L

    MHB Visualization of Integration by Parts

    Hello all, I am trying to understand the rational behind the visualization of integration by parts, however I struggle with it a wee bit. I was trying to read about it in Wiki, this is what I found...
  50. H

    Faraday's law with Calc 3 integration help

    Homework Statement Suppose an infinitely long wire carrying current ##I=sin_0(\omega t)## is a distance ##a## away from a equilateral triangular circuit with resistance ##R## in the same plane as shown in the figure. Each side of the circuit is length ##b##. I need to find the induced voltage...
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