Integration Definition and 1000 Threads

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. 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...
  2. 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=...
  3. 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...
  4. 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?
  5. 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...
  6. 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...
  7. 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 +...
  8. 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...
  9. 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...
  10. 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...
  11. 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...
  12. 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...
  13. 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...
  14. 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...
  15. 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...
  16. 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...
  17. Feodalherren

    ME statics shear/moment diagrams through integration

    Homework Statement Homework Equations w=(2/3)x The Attempt at a Solution So integrating w to get V (1/3)x^2 +C Then Sum in the Y-direction should be 9-(2/3)x+18=0 Somebody tell me what in god's name is going on here. It seems like they are ignoring the 18kN force and then plugging in my...
  18. Hijaz Aslam

    Electric Field of a circular arc at a point

    Homework Statement Given that the circular arc wire with radius 'r' has a linear charge density ##\lambda##. What is the Electric field at the origin? Homework Equations ##\vec{E}=\frac{kq}{r^2}## where ##k=9\times10^9## is a constant. 3. The Attempt at a Solution I took a small segment dy...
  19. S

    Proof of disk moment of inertia using area density

    Homework Statement Disk with radius R σ = M/A I = ∫ mr2 Homework Equations Today we learned how to derive various moments of inertia via density equations (M/L, M/A, M/V). I understand all of them except on how to get MR2/2 for a disk. The Attempt at a Solution I = ∫mr2 σ = M/A dM =...
  20. MartinJH

    Integration of a polynomial problem

    Hi, I'm using KA Stroud 6th edition (for anyone with the same book, P407) and there is a example question where I just can't seem to get the answer they have suggested: Homework Statement [/B] Question: Determine the value of I = ∫(4x3-6x2-16x+4) dx when x = -2, given that at x = 3, I = -13...
  21. A

    Solving Integrals using summations

    Homework Statement Many places I have seen when solving integrals you change a lot of it into sums. http://math.stackexchange.com/questions/1005976/finding-int-0-pi-2-dfrac-tan-x1m2-tan2x-mathrmdx/1006076#1006076 Is just an example. So in general, how do you solve integrals (CLOSED FORM) by...
  22. C

    MHB Finding new limits of integration problem

    In the integral integral(1,infinity) e^(-sqrt(x)) / sqrt(x) STEP 1: I let u = -sqrt(x) du = -1/(2sqrt(x)) then my lower bound u = -1 then my upper bound u = -infinity -2 integral(-1,infinity) e^u du I would then switch the order of the integration bounds and multiply by -1My question is...
  23. C

    Numerica integration with unequal intervals

    Hello, I have to compute the numerical integral of a function which is expressed at unequal (but almost) intervals. I tried the trapezoidal method, but the error is too large for my application. Is it possible to generalize the Boole's rule to or something on the same order of precision?
  24. P

    Integration by special technique

    Mentor note: Thread was moved to homework section Hello Folks I have integral ∫0π/2 (sinx/sinx+cosx) dx I have got the answer is π/4 I have even solved indefinite integral [ln(tan^2(x/2)-2(tan(x/2))-1)]/2 + [tan-1(tan(x/2)) + [ln(1+tan^2(x/2))]/2]/2 my problem is I am not getting pi/4 as...
  25. A

    Trying to find the infinite sum of e^-x using integration

    Hello, I am well aware of the ratio method, and the sum = 1/(1-r) but I want to try this method. I am trying to understand this: \displaystyle \sum_{n=1}^{\infty} e^{-n} using integrals, what I have though: = \displaystyle \lim_{m\to\infty} \sum_{n=1}^{m} e^{-n} = \displaystyle...
  26. B

    Integration using Euler Substitution

    Does anyone know of a derivation or justification of Euler's substitution formulas for evaluating irrational expressions? In other words, to evaluate integrals of the form: \int R(x,\sqrt{ax^2+bx+c}) You can use Euler's substitutions: 1. \sqrt{ax^2+bx+c} = t \pm \sqrt{a}x, a>0 2...
  27. K

    Grassmann Integration: Clarifying Notation in "hep-th/0108200

    Hi, everyone! I am trying to understand notation of this textbook http://arxiv.org/abs/hep-th/0108200 page 8, formulas 2.1.4 and 2.1.5 $$\int d \theta_\alpha \theta^\beta=\delta_\alpha^\beta$$ this could be found in any textbook the weird that from the above formula follows $$\int d^2...
  28. P

    Lower and Upper Riemann sums of sin(x)

    Task in real analysis: P is a uniform partition on [0, π] and is divided into 6 equal subintervals. Show that the lower and upper riemann sums of sin (x) over P is lesser than 1.5 and larger than 2.4 respectively. My attempt at the solution: The greates value and the least value of sin x over...
  29. P

    2D Milne's rule composite integration

    http://en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas Simpson rule: 1 4 1, and the composite version: 1 4 2 4 2 4 2 4 ...4 1 in a double integral we just compute rows, and next columns, a this gives a matrix: http://mathfaculty.fullerton.edu/mathews/n2003/SimpsonsRule2DMod.html Milne's...
  30. E

    Lubrication Theory: Fluid Flow and Integration

    Basically, I'm modelling the flow of a "coating" process -- a fluid flow between a flat moving plane and a stationary cylinder, 2D, cartesian coordinates. Subscript 0 is the at the minimum height b/w the plane and the cylinder, and subscript c is at the point at which the flow leaves the moving...
  31. H

    W=F.dx rate of change of x approaches to zero?

    In the integration of Force with respect to displacement (W=∫F.dx), is that true if the rate of change of displacement approaches to zero? My teacher said the one which approaches to zero is the rate of change of time. But If I arrange the formula, I will get F=dW/dx then F= lim Δx→0 ΔW/Δx...
  32. B

    Thermodynamics atmospheric pressure Question

    Homework Statement A liter of air, initially at room temperature and atmospheric pressure, is heated at constant pressure until it doubles in volume. Calculate the increase in its entropy during this process. so Ti= 300K, Volume which is 2Vi=Vf; Pressure is constant Homework Equations ΔS...
  33. M

    Solution to Hydrostatic Bearing Integration Task

    Hi everyone! I would like to ask you for help with one of the tasks from my assignment. The rest of the assignment is done including some simple integration but I struggle with this one: Task "The total load capacity for a circular hydrostatic bearing is given as ##W=\int_0^{R_o} p_r(2πr dr) +...
  34. L

    Integration: force on submerged triangular plate

    Homework Statement Submerged (vertically) right triangle 12x9x15(hypotenuse) with 12 m leg parallel to water surface. Top of triangle is 3m below surface. Find force on triangle.[/B]Homework Equations I know mass of water is 840 k/m3. I think I should also multiply times 9.8 for gravity...
  35. J

    How to integrate this one P(x1<x2<x3<1)

    Homework Statement Let f(x1, x2, x3) = e-(x1+x2+x3), 0<x1,2,3<infinity, zero elsewhere be a joint pdf of X1, X2, X3. The variables are all independent to each other Compute P(X1< X2< X3|X3<1 ) Homework Equations P(X1< X2< X3|X3<1 ) The Attempt at a Solution P(X1< X2< X3|X3<1 )=P(X1< X2< X3<1...
  36. D

    Solve Equation with No Analytic Solution - Symbolic Integration

    I would like to solve an equation: NIntegrate[f[x],{x,a,b}]==1 For a and b, my function doesn't have analytic solution.
  37. M

    Sensor - accelerations to displacements, error

    Hello everybody, apologies from outset for bad English. I wonder if anyone can give me some advice regarding my problem. I have a sesnor that gives acceleration readings. I have been working hard to turn these readings into position or displacements. I tried many method but MATLAB cumptrapz...
  38. L

    Finding volume of a nose cone with a given r with integration

    I'm still confused on some of these volume problems, so please bear with me :) Homework Statement Find the volume of a reentry spacecraft nose cone that has a cross-section radius of (1/4)x2 taken x feet from the nose and perpendicular to the axis of sym. We are given that the length of...
  39. M

    Is There a Simple Solution for This Integral?

    for the problem: \int {[(y-1)^3 + C]^{-1/2}}dy Is there a simple solution that can yield an answer? C is a constant. Integration by parts doesn't seem to look helpful (at least to me). Trigonometric substitution looks like one method that would work, though it would involve quite a bit of...
  40. D

    MHB Can you help me solve this tricky integral involving arctanx?

    Hello everyone! I need some help with the integral: $\displaystyle \int \dfrac{1}{\tan^{-1}(x)}dx$ I don't know how to solve it... can you guys help me please?
  41. P

    Numerical integration of a function specified numerically

    Dear All, Can someone suggest me an appropriate routine (in Fortran) or command (in mathematica) to perform numerical integration of a function, which is specified numerically on a one dimensional grid with equal spacing (and we cannot generate additional data on other grid points)? There are...
  42. H

    Definite Integrals Using Contour Integration

    Problem Show: \int_0^\infty \frac{cos(mx)}{4x^4+5x^2+1} dx= \frac{\pi}{6}(2e^{(-m/2)}-e^{-m}) for m>0 The attempt at a solution The general idea seems to be to replace cos(mx) with ##e^{imz}## and then use contour integration and residue theory to solve the integral. Let ##f(z) =...
  43. M

    How Can Set-Valued Maps Be Integrated in Measurable Spaces?

    laTex
  44. M

    Measurability and integration of set-valued maps

    What is the difference between the measurable set-valued maps and measurable single-valued map? What is the difference between the integrable set-valued maps and integrable single-valued map? With illustrative examples, if possible? Thank you very.
  45. A

    Normal force of real pulley: Which direction is it?

    Consider a pulley fixed to the ceiling. A mass-less string is wrapped around it, with each side of the string hanging down either side of the pulley. Since the pulley has friction with the string, tension along the string will vary. Let's say the string is attempting to move clockwise, so the...
  46. L

    Calculating Arc Length of a Curve: A Calculus II Problem

    Homework Statement Find the exact length of the curve: y= 1/4 x2-1/2 ln(x) where 1<=x<=2 Homework Equations Using the Length formula (Leibniz) given in my book, L=Int[a,b] sqrt(1+(dy/dx)2) I found derivative of f to be (x2-1)/2x does that look correct? The Attempt at a Solution I found f'...
  47. B

    Volume of solid x^2 + (y-1)^2 =1 about y-axis

    Homework Statement Hello, I am to find the volume of the solid given by x2 + (y-1)2=1 rotated about the y-axis. I may use either shells or cylindrical method. I attempted shell method, but am just learning this, still foggy and this is the one question that isn't coming out right. Homework...
  48. C

    Integrating ##d\psi=(x+y)dx +x_0dy##

    I am quite embarrassed to ask this question, as I know i have lost track of the concept here, but Ill nevertheless ask it. I was going through Mathematical methods for physicists (pg 333), and there was an example: "Solve $$y'+(1+\frac{y}{x}) = 0$$" My problem is, (a) when you put the...
  49. A

    MHB Integration using Beta and Gamma Functions

    Interestingly, I seem to have an integral I have posted before, but I want to take a different approach to it. $\int_{0}^{1} \frac{\ln(1+x)}{1+x^2} \,dx$ The beta function states, $B(x,y) = \int_{0}^{1} {t}^{x-1}({1-t}^{y-1}) \,dx$ So, I was just thinking if there a possible way to compute...
  50. M

    MHB Advanced Integration techniques Needed

    Hi I have the integral $G(x,y)=\int_{0}^{2\pi}d\theta\frac{1}{\sqrt{a_1\cos(2\theta)+a_2\sin(2\theta)+1}}\frac{1}{x\cos(\theta)+y\sin(\theta)}$I broke it into two terms in the hopes of simplifying the integrand...
Back
Top