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.

View More On Wikipedia.org
Recent contents Top users
  1. M

    Integration by Parts: Does the Choice of u and dv Matter?

    Homework Statement $$ \int x^{3}cos(x^{2})dx$$ The attempt at a solution OK, so I am aware that there is a way in which to do this problem where you do a substitution (let $$u=x^{2}$$ to do a substitution before you integrate by parts), and I was able to get the answer right using this method...
  2. L

    Corollary 8: Integration in 'Polar Coordinates'

    I am reading Spivak's Differential Geometry Vol. 1. I am stuck for some days in chapter 8 about integrating forms on manifolds. Maybe someone can clear my doubt. First, I will 'type' what the corollary says: My doubt is regarding this affirmation: The book it says is easy to see. Well...
  3. G

    Jefimenko's Equations: Integrals & Integration

    http://en.wikipedia.org/wiki/Jefimenko's_equations What is the integral in these equations called? how do you integrate over (d^3)r'?
  4. R

    Finding Solutions to a Step Function Integral

    Homework Statement This is from Apostol's Calculus Vol. 1. Exercise 1.15, problem 6.(c) Find all x>0 for which the integral of [t]2 dt from 0 to x = 2(x-1) Homework Equations [t] represents the greatest integer function of t. The Attempt at a Solution [/B] Integral of [t]2 dt from 0 to x...
  5. F

    Help with an intermediate integral

    Homework Statement I have been trying to evaluate an integral that has come up in the process of me solving a different problem, but am completely stuck. As I have confirmed with Wolfram Alpha that the integral once solved yields the correct solution to my problem. However, I am trying to...
  6. A

    Calculating Harmonic Sums using Residues

    I posted the same question on Math Stackexchange: http://math.stackexchange.com/questions/1084724/calculating-harmonic-sums-with-residues/1085248#1085248 The answer there using complex analysis is great. I had questions, which Id like to get advice on here. (1) How did he get the laurent...
  7. A

    MHB Evaluating a rational function with contour integration

    Hello, I am looking to evaluate: $$I = \int_{0}^{1} \frac{x^4(1-x)^4}{1+x^2} dx$$ I will use a rectangular contour. The image looked weird here so the upload of the image is here: http://i.stack.imgur.com/W4BfA.jpg $R$ is more like the radius of the small semi circle, we have to let $R \to...
  8. P

    Arc Length: Definite and Indefinite Integration

    Several authors state the formula for finding the arc length of a curve defined by ##y = f(x)## from ##x=a## to ##x=b## as: $$\int ds = \int_a^b \sqrt{1+(\frac{dy}{dx})^2}dx$$ Isn't this notation technically wrong, since the RHS is a definite integral, and the LHS is an indefinite integral...
  9. J

    Fourier sine series integration

    Homework Statement The question is to get Fourier sine series of e^-x =f(x) on 0<x<1 Homework Equations Bn = 2/L ∫ (e^-x) * sin(nπx/L) over the limits 1 to 0, where L = 1 f(x) = summation of Bn*sin(nπx/L) The Attempt at a Solution So I integrated ∫ by part integration so I took u =...
  10. F

    Convergence of Integral with Real and Imaginary Parameters

    The integral given below is to be computed as a function of real variables x and s. Even a partial answer only for s>0 is very useful. Here is the integral: $$\int_{0}^{\infty}{dk \frac{k^2 e^{-k^2 x^2}}{(k^2 + s)^{3/2}}}$$ Thank you for your help.
  11. A

    MHB Complex Contour Keyhole Integration Methods

    This is an interesting complex analysis problem; **The figure on the bottom left is what is being referred to,Fig7-10.** **Firstly: (1)** How is the branch point $z=0$ at $z=0$?? We have $f(0) = 0$ that is not a discontinuity is it? **Secondly:(2)** It says that: $AB$ and $GH$ are coincident...
  12. QPingy

    Numerical integration - verlet algorithm - accuracy

    In my computational physics textbook, three different velocity estimators are derived for a problem with equation of motion: \ddot x = F(x) where the positions are found by using the Verlet algorithm: x(t+h) = 2 x(t) - x(t-h) + h^2 F[x(t)] The three velocity estimators are: v(t) = \frac{x(t+h)...
  13. A

    MHB Complex Contour integration of rational function

    Hello, Evaluate: $$\int_{0}^{\infty} \frac{\cos(x)}{x^2 + 1} dx$$ We know that because $f(x)$ is even:$$\int_{0}^{\infty} \frac{\cos(x)}{x^2 + 1} dx = \frac{1}{2} \cdot \int_{-\infty}^{\infty} \frac{\cos(x)}{x^2 + 1} dx$$ Consider a complex function, with $z = x + iy$ $$f(z) =...
  14. J

    Exponential integration confused

    Hi, does anyone know how to integrate e^-x (sin(nπx))? I have tried part integration but that goes on until infinity... and I am not sure how to use the substitution method...Please help! I have tried taking e^-x as U but then I end up getting the entire canceled off then...
  15. B

    Which Integral Calculation is Correct?

    Homework Statement Which one is correct? ##\int (3x+2) (2x+1)^{\frac{1}{2}} dx = \frac{1}{3} (3x+2)(2x+1)^{\frac{3}{2}} - \frac{1}{15} (2x+1)^{\frac{5}{2}} + C## or ##\int (3x+2) (2x+1)^{\frac{1}{2}} dx = \frac{1}{3} (3x+2)(2x+1)^{\frac{3}{2}} - \frac{1}{5} (2x+1)^{\frac{5}{2}} + C## ...
  16. J

    Heat equation problem so confusing

    Homework Statement The problem is f(x) = sin2πx - (1/πsquare)*sinπx and its given Bn sin (nπx) = f(x) Question is find Bn. Homework Equations Bn = 2/L ∫ (sin2πx - (1/πsquare)*sinπx) * sin(nπx/L) where L is 1 The Attempt at a Solution I did [/B] ∫ sin2πx * sin (nπx) - (1/πsquare)*sin...
  17. J

    Solve Wave Equation: e^(-x^2), x*e^(-x^2), -infinity<x<infinity

    Homework Statement So it says solve this wave equation : [y][/tt] - 4 [y][/xx] = 0 on the domain -infinity<x<infinity with initial conditions y(x,0) = e^(-x^2), yt(x,0) = x*(e^(-x^2)) Homework Equations I used the D Alembert's solution which is 1/2(f(x+ct)+f(x-ct)) + 1/2c ∫ g(z) dz The...
  18. T

    How Can I Find the PDF Along One Axis for Exponential Decay in 2D Space?

    I'll like to know the probability density function for one of the x or y axis, given that there is an exponential decay of a material in two-dimensional space. So, that means I have to marginalize, say y and keep x, but I couldn't solve the integration. I even tried with Mathematica and Matlab...
  19. V

    Integration constants, gravitational potential of sphere

    Homework Statement So I'm calculating the gravitational potential of a sphere at at point P. R = radius of sphere, r = distance from center of sphere to point P. I'm looking at two scenarios; r > R (1) and r < R (2). So I have the following integral: \begin{equation} V(r) = \int...
  20. Z

    Volume of a Solid Revolved About X-Axis

    I'm trying to practice for my final. The sample problem is: "Find the volume of the solid generated when the region bounded by y = x4and y = x1/3, 0<=x<=1, is revolved about the x-axis." To start, I set the two y equations equal to each to find the points of intersection. x4 = x1/3, : raise...
  21. M

    Checking if Momentum Operator is Hermitian - Integration

    Homework Statement I'm checking to see if the momentum operator is Hermitian. Griffiths has the solution worked out, I'm just not following the integration by parts. Homework Equations int(u dv) = uv - int(v du) The Attempt at a Solution I've attached an image of my work. It seems there...
  22. SalfordPhysics

    Comp Sci Fortran90: DO loop for sequence of numbers

    Homework Statement A program finds the area under the Gaussian Distribution Curve between ±σ using Simpsons Rule. Modify the program to investigate the effect of the number of strips. Do this by using a DO loop in the main program for the following sequence of number of strips (n); n-2, n-4...
  23. B

    Integration of x^{-4}y' - 4x^{-5}y = xe^x: Solution and Explanation

    Homework Statement Solve: ##x \frac{dy}{dx} - 4y = x^6 e^x.## Solution: Dividing by ##x##, we get the standard form ##\frac{dy}{dx} - \frac{4}{x}y = x^5 e^x.## Hence the integrating factor is ##e^{\int -\frac{4}{x}dx}= e^{-4 \int \frac{1}{x}dx} = e^{-4 \ln x} = e^{\ln x^{-4}} = x^{-4}##...
  24. S

    Use of substitution for integration

    I was wondering if there is a convenient way of checking if a substitution is correct or not. For example, I tried solving for ∫(1/(a^2-x^2)dx using two different substitutions, x=acosu and x=asinu giving different solutions. I got the integral as arcsin(x/a) using x=asinu and -arccos(x/a) using...
  25. M

    What is the Equation for Water Pressure on a Dam Wall?

    Homework Statement Consider a simple model of a free-standing dam, depicted in the diagram. Water of density ρ fills a reservoir behind the dam to a height h. Assume the width of the dam (the dimension pointing into the page) is w. (a) Determine an equation for the pressure of the water as...
  26. N

    Integrate x^(5/2) e^(-x): Solving w/ Substitution & √2π

    Homework Statement Using \int_{-\infty}^{\infty}e^{-x^2/2} dx = \sqrt{2\pi}, Integrate x^(5/2) e^(-x) dx from 0 to infinty 2. The attempt at a solution I tried substituting x = u^2/2 but i could not simplify further. Please help me with the problem. Thank you in advance.
  27. little neutrino

    Solving Electric Field of an Insulating Slab

    Homework Statement A slab of insulating material has thickness 2d and is oriented so that its faces are parallel to the yz-plane and given by the planes x = d and x = -d. The y- and z- dimensions of the slab are very large compared to d and may be treated as essentially infinite. Homework...
  28. I

    MHB Integration and Differentiation

    Evaluate ∫[sin2x/(1+(cos)^2 x) dx]Differentiate f(x) = (sin)^2 (e^((sin^2) x)) Hello, I'm just really stumped with these review questions and i have a test coming up. For the first, I'm not too sure what to do since there is a sin2x in general and for the second i don't know how to deal the...
  29. DivergentSpectrum

    Is the Alternative Method for Integration by Parts Simpler?

    I have a question why everyone says ∫uv' dx=uv-∫u'v dx why don't they replace v' with v and v with ∫vdx and say ∫uv dx=u∫vdx-∫(u'∫vdx) dx i think this form is a lot simpler because you can just plug in and calculate, the other form forces you to think backwards and is unnecessarily complicated.
  30. T

    Limits of integration

    Homework Statement sketch the solid region contained within the sphere, x^2+y^2+z^2=16, and outside the cone, z=4-(x^2+y^2)^0.5. b) clearly identifying the limits of integration, (using spherical coordinates) set up the iterated triple integral which would give the volume bounded by the...
  31. B

    Solving Difficult Integrals: Step by Step Guide

    Homework Statement ##(e^y + 1)^2 e^{-y} dx + (e^x + 1)^3 e^{-x} dy = 0## Homework EquationsThe Attempt at a Solution ##(e^y + 1)^2 e^{-y} dx + (e^x + 1)^3 e^{-x} dy = 0## ##(e^{2y} + 2 e^y + 1) e^{-y} dx + (e^{3x} + 3e^{2x} + 3e^x + 1) e^{-x} dy = 0## ##(e^{2y - y} + 2 e^{y - y} + e^{-y}) dx...
  32. gracy

    Integration Constant in Physics: When to Use It?

    I have not taken maths so you may find my question silly. in physics i have to deal with integration.so can you please tell me where we write integration constant and where we don't?
  33. B

    Need help with Schrödinger and some integration

    My wave function: ##\psi_2=N_2 (4y^2-1) e^{-y^2/2}.## Definition of some parts in the wavefunction ##y=x/a##, ##a= \left( \frac{\hbar}{mk} \right)##, ##N_2 = \sqrt{\frac{1}{8a\sqrt{\pi}}}## and x has an arrange from ##\pm 20\cdot 10^{-12}##. Here is my integral: ##<x^2> =...
  34. T

    Integration seems gaussian but the answer does not match

    Homework Statement -h^2/2m (sqrt(2b/pi)) e^(-bx^2) d^2/dx^2 (e^(-bx^2)) dx from - to + infinity Homework Equations I tried differentiating e^(-bx^2) twice and it came up weird , I positioned the values and finally cam up with (-2b sqrt(pi/2b)...is there any other way to do it ? The...
  35. samgrace

    How Can You Solve a Complex Numerical Integration Problem on Paper?

    Homework Statement Integreate: ##T = ∫ \frac{dy}{V_ab (y)} = \frac{2}{v}∫[1 + \frac{\alpha^2 y}{L} + 2\alpha \sqrt\frac{y}{L} cos(\phi(y))]^\frac{-1}{2} dy## where ## \phi (y) = \frac{\pi}{6} + sin^-1(\frac{\alpha\sqrt{y}}{2\sqrt{L}}) ## The limits are between 0 and L Homework EquationsThe...
  36. D

    Splitting up an interval of integration

    How does one prove the following relation? \int_{a}^{b}f(x)dx= \int_{a}^{c}f(x)dx + \int_{c}^{b}f(x)dx Initially, I attempted to do this by writing the definite integral as the limit of a Riemann sum, i.e. \int_{a}^{b}f(x)dx=...
  37. kelvin490

    Question about substitution method in integration

    It is common that we replace \int u(x)v'(x)dx by \int udv where both u and v are continuous functions of x. My question is, must we ensure that u can be written as a function of v before applying this? The above substitution method is involved in the proof of integration by parts but I cannot...
  38. ubergewehr273

    Integration in Calculus: Understand What It Is

    I have seen in a lot of textbooks this funny curly bar which denotes integration with a lot of fancy numbers around. Could anyone tell me what exactly is integration in calculus?
  39. G

    Evaluation of fugacity (Chemical Engineering)

    Homework Statement I was revising the topic on the evaluation of fugacity of liquids and gases for my chemical engineering course, when I ran into an equation which I think, may be wrong as I think it may evaluate to ln0, which is infinity. Here is a snapshot of the equation: The equation...
  40. S

    How are integration skills tested on GRE Mathematics Subject Test?

    Although it gets better with experience, integrating an expression by hand is a really a trial and error procedure. A wrong substitution will get you nowhere in the available time. So I am wondering as to how they test your integration skills on GRE Mathematics Subject Test. Any help would be...
  41. S

    Topic: Is there a solution to this infinite integration problem?

    Homework Statement Evaluate the limit 1 1 1 lim ∫ ∫ ... ∫ cos^2((pi/2n)(x1 + x2 +... xn))dx1 dx2 ... dxn 0 0 0 n→∞Homework Equations Well, I know that we can change this using a double angle rule, so that the integrals become 1/2 + 1/2 cos (2*pi/2n)(x1 +...
  42. bananabandana

    Two variable function, single integral

    Homework Statement Evaluate: I(y)= \int^{\frac{\pi}{2}}_{0} \frac{1}{y+cos(x)} \ dx if y > 1 Homework EquationsThe Attempt at a Solution I've never seen an integral like this before. I can see it has the form: \int^{a}_{b} f(x,y) dx I clearly can't treat it as one half of an exact...
  43. M

    Terrible experience in first integration (lebesgue) class

    Hello. I am in an undergraduate math major in an introductory graduate class on integration theory and it has truly been an unpleasant experience. I feel the instructor(who is teaching it for the first time) is pretty much completely disconnected from the students in his assignments and...
  44. B

    Integration - Change of Variable

    Homework Statement [/B] Use integration by substitution to evaluate the integral, I = \int^{x}_{x_{0}} (3 + 4t)^{\frac{5}{3}} dt Homework EquationsThe Attempt at a Solution I am confused by this question, and think that the limits on the integral might be a typo. Does it make sense for them...
  45. C

    Physics Major Struggles with Integration: Books to Help

    As a physics major, I felt devastated today when I had to face the toughest integrals in my life for advanced quantum mech course. I am really embarrassed I did bot learn integration properly. please suggest me a good book that will help me excel in sort of integraion I will face for QM and...
  46. C

    Integral physics, me understand a thing with respect to integration

    Hi, I'm trying to understand why When you write a*dt = dv then you can write the integral like this., ∫dv (from v0 to vt) = ∫a*dt (from 0 to t) My challenge is this: from the equation a*dt = dv, the term "dv" geometrically means an infenitesimalle small change in function value of the...
  47. jeffer vitola

    MHB Integration of function highly oscillating

    ,.,.,.hello to all forum users, I would like to know how to show or come to the solution of this oscillatory integral wolfram alpha program does not give the correct solution, I hope will be a real challenge for you,,. greetings from Colombia.,.,.,,..,,,...Integrate[ Sin[E^x^(4)], {x, 2...
  48. A

    MHB Concept of contour integration and integration along a square

    Hello, My question is, there is a concept of contour integration. Which is choosing a circular contour space sort of, and integrating along that. How do you do contour integration? Secondly, there is something going around called integrating along a square. I tried searching only, a lot...
  49. K

    MHB On integration, measurability, almost everywhere concept

    Suppose $\int f d\mu < \infty.$ Let $$h(\omega)=\begin{cases}f(\omega) \ \ \ \text{if} \ \ f(\omega)\in \mathbb{R} \\ \\ 0 \ \ \ \text{if} \ \ \ f(\omega)=\infty\end{cases}$$ How to show $h$ is measurable and $\int f d\mu = \int h d\mu?$ **Attempt:** It is known that the product of two...
  50. W

    Complex analysis: residue integration question

    I'm asked to evaluate the following integral: \int_{c} \frac{30z^2-23z+5}{(2z-1)^2(3z-1)}dz where c is the unit circle. This function has a simple pole at z=\frac{1}{3} and a second order pole at z=\frac{1}{2}, both of which are within my region of integration. I then went about computing the...
Back
Top