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.

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  1. J

    MHB Definite Integration: $$\int^{\frac{\sqrt{5}+1}{2}}_{1}$$

    Evaluation of $$\int^{\frac{\sqrt{5}+1}{2}}_{1}\frac{x^2+1}{x^4-x^2+1}\ln\left(x-\frac{1}{x}+1\right)dx$$
  2. S

    A Function integration of a Gaussian integral

    Consider the partition function ##Z[J]## of the Klein-Gordon theory ##Z[J] =\int \mathcal{D}\phi\ e^{i\int d^{4}x\ [\frac{1}{2}(\partial\phi)^{2}-\frac{1}{2}m^{2}\phi^{2}+J\phi]} =\int \mathcal{D}\phi\ e^{-i\int d^{4}x\ [\frac{1}{2}\phi(\partial^{2}+m^{2})\phi]}\ e^{i\int d^{4}x\...
  3. Prof. 27

    Solve Difficult Integral: ∫ex t-2 dt

    Homework Statement Hi, I'm doing a variation of parameters problem for my differential equations class. It requires solving the integral: ∫ex t-2 dt I am sure my professor did not give me an impossible integral and that there is some algebraic "trick" to solving it, but despite going through...
  4. S

    A Integration using delta function and step function

    I would like to evaluate the following integral: ##\displaystyle{\int_{-\infty}^{\infty} dp^{0}\ \delta(p^{2}-m^{2})\ \theta(p^{0})}## ##\displaystyle{= \int_{-\infty}^{\infty} dp^{0}\ \delta[(p^{0})^{2}-\omega^{2}]\ \theta(p^{0})}## ##\displaystyle{= \int_{-\infty}^{\infty} dp^{0}\...
  5. F

    I Contour integration - reversing orientation

    I have been reading through "Complex Analysis for Mathematics & Engineering" by J. Matthews and R.Howell, and I'm a bit confused about the way in which they have parametrised the opposite orientation of a contour ##\mathcal{C}##. Using their notation, consider a contour ##\mathcal{C}## with...
  6. sammyqw

    Engineering Circuits 1 help with integration

    Homework Statement http://imgur.com/a/qlQ5z Homework Equations i=i(o)+1/L integration(v0) dt formula is in the attemp at a solution. The Attempt at a Solution http://imgur.com/a/HVjl1 For the interval 2<t<infinite . I understand...
  7. nysnacc

    Triple integration over portion of Sphere

    Homework Statement Homework Equations spherical Jacobean The Attempt at a Solution I have (sorry, have to capture my work, too hard to type) then the integration of p3 ep2 = 1/2 ep2 (p2-3/2) ??
  8. A

    Calculus of Variations: Functional is product of 2 integrals

    Homework Statement Minimize the functional: ∫01 dx y'2⋅ ∫01 dx(y(x)+1) with y(0)=0, y(1)=aHomework Equations (1) δI=∫ dx [∂f/∂y δy +∂f/∂y' δy'] (2) δy'=d/dx(δy) (3) ∫ dx ∂f/∂y' δy' = δy ∂f/∂y' |01 - ∫ dx d/dx(∂f/∂y') δy where the first term goes to zero since there is no variation at the...
  9. Tspirit

    A problem on calculus in Griffiths' book

    I can't understand the solution to Problem 1.4(a). The solution is the following: What puzzles me is that ρ(θ)dθ=ρ(x)dx ? Why are they equal?
  10. E

    I Decomposing a Function for Numerical Integration

    Is their a tutorial or a reference on how to decompose a function, specifically Fourier and Legendre decomposition, for numerical integration? The method I am going to use for the numerical integration is the Gauss Quadrature, and I suppose I need to decompose my function for the rule to work...
  11. Elvis 123456789

    Integration by parts and approximation by power series

    Homework Statement An object of mass m is initially at rest and is subject to a time-dependent force given by F = kte^(-λt), where k and λ are constants. a) Find v(t) and x(t). b) Show for small t that v = 1/2 *k/m t^2 and x = 1/6 *k/m t^3. c) Find the object’s terminal velocity. Homework...
  12. C

    Solving a Double Integration Problem with Unknown Variables: How to Proceed?

    Homework Statement in this problem , i couldn't express all the x any y in terms of u( refer to the circled part ) ... so , i have problem to proceed my subsequent steps ... Homework EquationsThe Attempt at a Solution i let u = (x^2) + (y^2) ... [/B]
  13. N

    MHB Integrating $$1-y^2$$: Simplifying Arcsins

    $$\int(1-y^2)^\frac{1}{2}\,dy$$ I did trig substitution $$y=\sin\theta$$ $$dy=\cos\theta\,d\theta$$ $$\int(1+\cos2\theta)d\theta$$ $$\arcsin\,y+\frac{1}{2}\sin(2\arcsin\,y)+c$$ How do I get rid of the arcsins?
  14. N

    MHB Integration Help 2: Solving Int. w/ Unknown Method

    I need some help with this integran $$\int\frac{2x^2}{2x^2-1}dx$$I can't seem to solve this using the techniques that I know. What method should I use?
  15. J

    MHB Compare volume formula to integration

    So I need to compare the results of the volume formula of a cylinder to the results of the integration. In geometry, you learn that the volume of a cylinder is given by V = πr2h, where r is the radius and h is the height of the cylinder. Use integration in cylindrical coordinates to confirm the...
  16. T

    I Integration Limits Changing in Double Integral Order Change

    For part of a proof of a differential equations equivalence, we needed to use that $$\int_0^t [\int_0^s g(\tau,\phi(\tau))\space d\tau]\space ds = \int_0^t [\int_\tau^t ds]\space g(\tau,\phi(\tau))\space d\tau$$ I understand that the order is being changed to integrate with respect to s first...
  17. ShayanJ

    Contour integration with a square root

    Homework Statement Find the value of the integral ## \int_0^\infty dx \frac{\sqrt{x}}{1+x^2} ## using calculus of residues! Homework EquationsThe Attempt at a Solution This is how I did it: ##\int_0^\infty dx \frac{\sqrt{x}}{1+x^2}=\frac 1 2 \int_{-\infty}^\infty dx \frac{\sqrt{|x|}}{1+x^2} ##...
  18. J

    Gaussian integration in infinitesimal limit

    Homework Statement Given the wave function of a particle \Psi(x,0) = \left(\frac{2b}{\pi}\right)^{1/4}e^{-bx^2} , what is the probability of finding the particle between 0 and \Delta x , where \Delta x can be assumed to be infinitesimal. Homework EquationsThe Attempt at a Solution I proceed...
  19. F

    A Numerical integration of motion

    Hi,I'd like to build a simulation (realtime) of space ships near a black hole (neutral, still or rotating possibly). Key features would be: 1) the ships are test particles that do not affect the metric a) possibly test rigid-bodies with GR consistent rotational DOF. 2) the ships can fire...
  20. N

    MHB Integrate $\int\frac{1}{x(x^2+1)}dx$ - Techniques & Help

    I used substitution but did not get a form I know how to integrate. What technique should I use here? $\int\frac{1}{x(x^2+1)}dx$ Thanks!
  21. M

    MHB Integration Problem - Can Someone Help?

    Can someone help with this problem, i tried to solve it using f'(x)/f(x) but couldn't figure it out.
  22. C

    MHB Why does the integral of √(a² +x²) need Integration by parts?

    Why this integral $\int\left\{\sqrt{{a}^{2}+{x}^{2}}\right\}dx$ needs integration by parts? Thanks Cbarker1
  23. user123897

    Java Numerical integration of an harmonic oscillator using java

    Hi, I am trying to analyze the an harmonic oscillator using kinematics. first i calculate the force applied by the spring (f = (-x)*k) then i calculate the acceleration (a = f/m) then speed (v= v0 + v0t + 0.5*a*t^2) and finally update x (x = x0+vt) this is a simplfied loop of my program...
  24. Prasun-rick

    I Volume of sphere using integration?

    Is it possible to find the volume of a sphere(i know the formula) using definite integration ? And if possible how to proceed ?? Thanks in advance
  25. A

    I Contour integration over Riemann surface

    Cauchy integral theorem states that the contour integration of a complex harmonic function along a closed simply connected path=0. What if this simply connected path is drawn over a Riemann surface of function like ##f(z)=\sqrt z##. Will that be possible in the first place? and will the...
  26. karush

    MHB S6.7.1.13 natural log Integration

    $\large {S6.7.1.13}$ $\tiny\text {natural log Integration}$ $$\displaystyle \int e^{\sqrt[3]{x}} \, dx = 3\left(x^\frac{2}{3} -2\sqrt[3]{x} +2\right){e}^\sqrt[3]{x}+C \\ u=x^{1/3} \therefore 3{x}^{\frac{2}{3}} du = dx $$ $\text{not sure if this is how to start to get to a 3 term answer}...
  27. micromass

    Insights Omissions in Mathematics Education: Gauge Integration - Comments

    micromass submitted a new PF Insights post Omissions in Mathematics Education: Gauge Integration Continue reading the Original PF Insights Post.
  28. A

    Difficult Separable Integration Problem

    Homework Statement Q=-1*K(T)*(H*W)*(dT/dx)+((I^2)(p)(dx)/(H*W)) K(T)=(197.29-.06333333(T+273)) H=0.01905 W=0.06604 I=700 p=10*10^-6 Q=some constant Please separate and differentiate to solve for Q using variables of T and x. Boundaries: T: Upper=T1 (constant) Lower=T0 (constant) x: Upper=L...
  29. D

    Designing a 5L Football for the MFL

    Homework Statement You have been employed but(sic) the Mathematics Football League (MFL) to design a football. Using the volume of revolution technique, your football design must have a capacity of 5L ± 100mL. You must present a statement considering the brief below. Just a quick side note, I...
  30. Virang807

    I Question about Hydrostatic Force?

    Hello! I am currently in Calculus 2 and we are dealing with hydrostatic force. I get the integration that happens but I always seem to have trouble with solving the word problems. With this problem, I realize that I use integrate by making an infinite number of rectangles on the 2 triangles. I...
  31. karush

    MHB How is Integration by Parts Applied to $\int_{0}^{\pi} x^3 \cos(x) \, dx$?

    $\Large {S6-7.1.24}$ $$ \displaystyle I=\int_{0}^{\pi} {x}^{3}\cos\left({x}\right)\,dx=12-3{\pi}^{2} \\ \begin{align} u& = {{x}^{3}} & dv&=\cos\left({x}\right) \, dx \\ du&={3x^2} \ d{x}& v&={\sin\left({x}\right)} \end{align} \\ $$ $$ \text{IBP} \displaystyle =uv-\int v\ du \\...
  32. H

    I Partial integration vs total integration and time-dependent force

    Integration as antiderivative Question: Why isn't a distinction made between anti-total-derivatives and anti-partial-derivatives in common usage of integration? Consider the functions ##G_1(x, t)## and ##F(x, t)## such that ##F(x, t)=\frac{d}{dx}G_1(x, t)=\frac{\partial G}{\partial...
  33. A

    I Integrating √(ex-3) with Substitution: Step-by-Step Guide

    I have been given the problem ∫√(ex-3) and we must use the substitution u = √(ex-3) I can start it off with u = √(ex-3) and du = exdx/2u and what I've been trying is to complete the square and go towards 2 ∫ u2du/((u2+4) -1) But I am not getting towards the answer, either I am doing...
  34. M

    Complex integration, possibly branch cut integral

    Homework Statement The integral I want to solve is $$ D(x) = \frac{-i}{8\pi^2}\int dr\,d\theta \frac{e^{-irx\cos\theta}}{\sqrt{r^2+m^2}}r^2\sin\theta$$ which I've reduced to $$ D(x) = \frac{-i}{4\pi x}\int dr \frac{r\sin(rx)}{\sqrt{r^2+m^2}} $$ by integrating over ##\theta##. However, I...
  35. H

    Arclength Problem; stuck on integration

    Homework Statement Find the arclength of $$r(t) = <{t}^2/2,{t}^3/3>$$ from t=-1 to t=1 Homework Equations I have used this equation for arclength $$\int_{-1}^{1}|{r}'(t)|dt$$ The Attempt at a Solution After integrating (using u substitution) I have the solution...
  36. micromass

    Insights Some Misconceptions about Indefinite Integrals - Comments

    micromass submitted a new PF Insights post Some Misconceptions on Indefinite Integrals Continue reading the Original PF Insights Post.
  37. karush

    MHB What is the Integration Formula for x and p in Maxima?

    $\Large{§8.8.15} \\ \tiny\text {Leeward 206 Integration to Infinity}$ $$\displaystyle \int_{e^{2}}^{\infty} \frac{dx}{x\ln^p\left({x}\right)}\,dx \,, p>1$$ $\text{not sure how to deal with this} $ $\text{since there are two variables x and p} $ $\text{answer by maxima is:'} $...
  38. MrKriss

    How can I derive J=pi*D^4/32 using integration?

    Homework Statement D1=6cm D2=2cm ( i have to prove that 2nd moment of area (J) of a circulal plate abouts its polax axis(zz) is equal to piD^4/32 ) Homework EquationsThe Attempt at a Solution J=pi6^4/32 - pi2^4/32 = 125.66 J=r1^2x2pirdr J=Integral 2pir^3d2 = 2pi integral(high 3 , low 1)...
  39. karush

    MHB How Does Integration to Infinity Work in Calculus?

    $$\Large{§8.8. 14} \\ \tiny\text {Leeward 206 Integration to Infinity}\\ \displaystyle I=\int_{2 }^{\infty} \frac{1}{x\ln\left({x}\right)}\,dx \\ \begin{align}\displaystyle u& = \ln\left({x}\right) & du&=\frac{1}{x} \ d{x} \end{align} \\ \displaystyle I=\int_{2}^{\infty}\frac{1}{u}...
  40. C

    Beam deflection integration help

    Homework Statement can someone explain about the RHS of EIy' and EIy'' ? how to get the RHS of EIy" from RHS of EIy' ?? It's not integration of dx , am i right? Homework EquationsThe Attempt at a Solution if it's integration of dx, it should look like this , right?[/B] EIy' = 0.25P(x^2) -...
  41. chwala

    Integrate e^x^2 + 2e^x^2x^2: Solution Explained

    Homework Statement ##∫e^x^2 + 2e^x^2x^2 dx##[/B]Homework EquationsThe Attempt at a Solution i let## u= x^2, ⇒ du = 2x dx, ⇒∫e^x^2 dx = e^x^2/2x ## is this correct? by using integration by parts.... i am getting ##xe^x^2-e^x^2/2x##
  42. chwala

    Deriving d/dx (ye^∫pdx): Integration Factor Homework

    Homework Statement ## d/dx (ye^∫pdx = Py+ y'e^∫pdx## now i know how they got ## y'e^∫pdx## . How do you differentiate ##ye^∫pdx## to get the first part i.e## Py ## presumably by product rule? Homework EquationsThe Attempt at a Solution [/B] d/dx of e^∫pdx is equal to P ...how?
  43. chwala

    Efficient Integration of Trigonometric Functions: Solving ∫ (1/sin 2x)dx

    Homework Statement [/B] ##∫ (1/sin 2x)dx##Homework EquationsThe Attempt at a Solution let ##u = sin 2x, ⇒ du= 2cos2x dx## or ##sin 2x= 2 sin x cos x##...[/B] or ##∫ (1/sin 2x)dx = ∫( csc 2x)dx##
  44. karush

    MHB LCC 8.8.11 Infinite Intervals of Integration

    $\tiny\text{LCC 206 8.8.11 Infinite Intervals of Integration}$ $$\displaystyle I=\int_{1}^{\infty} {x}^{-2} \,dx = 1$$ $$I=\left[\frac{1}{x}\right]_1^\infty=\left| 0-1 \right|=1$$ $\text{the only way apparently to get 1 is to use absolute value ?}$ $\tiny\text{from Surf the Nations math study...
  45. G

    B What is the integral of 1/2sin(2pi/n)(r^2-z^2) dz

    The answer here shows the answer as being but my limited knowledge of integrals begs me to asks where did the z go?
  46. N

    MHB Solve Integration Problem - Get Help Now!

    Hello can you help solve this problem \int_{}^{}\frac{ds}{\sqrt{s^2-0.01}} I tried using method of substitution but I still could not find a good cancellation. Please tell me what to do. Thanks!
  47. Electgineer99

    Understanding Integration by Parts: Exploring the Formula and Solving Examples

    |3^xlog3dxI don't even know where to start. I know that the formula is |u.dv = uv - |v.du u=3^x v=log3
  48. Destroxia

    Volume Integration Around Non-Coordinate Axis

    Homework Statement Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 5. (Use disk method) $$ xy = 3, y = 1, y = 4, x = 5 $$ Homework Equations [/B] The formula using for disk method is of the form: $$ \pi \int...
  49. M

    How Do You Solve This Complex Integration Problem?

    I need some help with an Integration. Here's the equation I = ##\int_0^∞ \frac {x^{n+1}} {1 + x^n} ⋅ e^{-x^2/{2 \sigma^2}} ## I have tried to solve the equation by simplifying first like let, ## \frac x {\sqrt 2 \sigma} = v ##, so the ##x = v \sqrt 2 \sigma## then, ##dx = \sqrt 2 \sigma d...
  50. P

    MHB Sava's question via email about integration with partial fractions.

    As there is a repeated root, the partial fraction decomposition we should use is: $\displaystyle \begin{align*} \frac{A}{x - 1} + \frac{B}{\left( x - 1 \right) ^2 } + \frac{C}{x - 2} &\equiv \frac{x^2}{\left( x - 1 \right) ^2\,\left( x - 2 \right) } \\ \frac{A\,\left( x - 1 \right) \left( x - 2...
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