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. Abtinnn

    A problem with Integration by Parts in Hartle's "Gravity"

    Hi guys! I am reading the book "Gravity" by Hartle. I came across this scary-looking integral. The author does integration by parts and I don't get how he does it. Could someone guide me please? Relevant equations: ∫u dv = uv - ∫v du
  2. Aceix

    Integrating a Definite Integral with an Undefined Function at One Endpoint

    Homework Statement integrate from 1 to 2 x(x^2-3)^(1/2) with respect to x. Homework EquationsThe Attempt at a Solution i attempted using numerical approximations but at x=1, the function is not defined so is there a way to combine improper integrals with this? Aceix.
  3. T

    Integration using u substitution

    Homework Statement Evaluate the integral of (x+1)5^(x+1)^2 Homework EquationsThe Attempt at a Solution I set my u=(x+1) making du=1dx. This makes it u*5^u^2. I integrated the first u to be ((x+1)^2/2) however I don't know what to do with the 5^u^2
  4. K

    Integration Homework: Substitution, Partial Fraction, By Parts

    Homework Statement integrate Homework Equations please solve this using methods only like 1. Substitution 2.Partial fraction 3.By Parts The Attempt at a Solution i have tried all the above three methods mainly using substitution and by parts... i have expanded the a^3 - x^3 and then kept...
  5. C

    Integrate 1/(1+e^x) dx: Solving the Problem

    Homework Statement integrate 1/(1+e^x) dx Homework EquationsThe Attempt at a Solution firstly i let t=1+e^x and then i come to : integrate 1/(t^2-1) and then i put t=secx . . . but then the final ans is -1/2 ln | 2/e^x +1 | it should be 1 instead of 2, i hv checked for the steps for so many...
  6. StrangeCharm

    Integration by Partial Fractions Help

    Homework Statement ∫ [x^(3)+4] / [x^(2)+4] dx Homework Equations N/A The Attempt at a Solution I know that the fraction is improper, so I used long division to rewrite it as x+(-4x+4)/[x^(2)+4]. Given the form S(x)+R(x)/Q(x), Q(x) is a distinct irreducible quadratic factor [x^(2)+4]. I used...
  7. Rapier

    Numerical Integration for Magnetic Field of a Loop of Wire

    Homework Statement Calculate the magnetic field of a current loop. Compare your numerical results with exact solution above the center of the loop. Investigate the effect of the grid size based on this comparison. Homework Equations dB = u0*I/4pi * (dL * R) / (R^2 + Z^2)^3/2 Bz = u0*I*R^2/ (2...
  8. D

    Integration of Multiple Variables

    Hi There, I'm a new member, so apologies if I've posted this in the wrong area. I've been working through the ASME STS-1-2006 Steel Stack Standard, particularly the Vortex Shedding section. I've come across this nasty integral which is doing my head in, and we wondering if anyone would mind...
  9. D

    Integrating Forms on Manifolds: Understanding the Concept and Techniques

    In all the notes that I've found on differential geometry, when they introduce integration on manifolds it is always done with top forms with little or no explanation as to why (or any intuition). From what I've manage to gleam from it, one has to use top forms to unambiguously define...
  10. AdityaDev

    Definite integral question

    Homework Statement $$\int_0^{\pi/2}(sinx-cosx)ln(sinx)dx$$ Homework Equations ##int_0^af(x)dx=int_0^af(a-x)dx## The Attempt at a Solution Using above equation, you get (without integral sign): ##(sinx-cosx)ln(tanx)## but it did not make any difference. I got the answer by splitting the...
  11. R

    Moment of inertia of half disk through integration

    Hello, sorry for this stupid question. I struggled to find the moment of inertia of half solid thin disk (about the center of the disk) through an integration, but I couldn't get the right value. I'm pretty sure it has to be MR^2/4, but I=\int r^2 dm \\ dm=(M/A)dS With A=\pi R^2/2 I compute...
  12. J

    Power rule of an integration [beginner]

    So I stumbled upon ∫1/(x^4) , and by applying the power rule , the answer is: -1/(3x^3) Why's that? Sorry for bothering you guys with such a beginner question!
  13. S

    Integration with limit of zero giving infinity - help please

    Homework Statement Integral of ∫1/x^2 (or ∫x^-2) between 1 and 0.The Attempt at a Solution I can integrate it no problem to give me -1/x or x^-1, but when I put it between the limits of 1 and 0 I get ∞-1 which is just ∞. Is this right or do I need to use L'Hopital's rule. If so, how? I'm...
  14. D

    Problem integrating gamma ray absorption model

    Homework Statement In this lab various thicknesses of a few materials are placed between a source of gamma radiation and a couple different detectors. It is reasonable to assume that some small change in the thickness of the shielding would produce a proportional change in the intensity of the...
  15. M

    Can anyone help me solve this Integration of three terms?

    I have been trying to solve an integration that i have I am not even sure if it's possible. Here, A, m, alpha, a these are constants. I have tried few methods, but couldn't find any way out. I would appreciate any help.
  16. T

    Integration of 1/4(x-2)

    Homework Statement Homework EquationsThe Attempt at a Solution i got ln(x-2) but not sure what to do with the 4[/B]
  17. D

    Addition property of integration intervals proof

    First of all, apologies as I've asked this question before a while ago, but I never felt the issue got resolved on that thread. Is it valid to prove that \int_{a}^{c}f(x)dx=\int_{a}^{b}f(x)dx+\int_{b}^{c}f(x)dx using the fundamental theorem of calculus (FTC)?! That is, would it be valid to do...
  18. J

    MHB How to Write an Answer for Integration with Logarithms?

    For example, \int \frac{e^x}{3e^x-1}dx, Should I write my answer in this \frac{1}{3}\ln (3e^x-1)+c or \frac{1}{3}\ln \left | 3e^x-1 \right |+c ?
  19. A

    Integration Using Trigonometric Substitution Help Needed

    Homework Statement Integral of $$ x^3\sqrt{x^2+16}dx $$ answer should give $$ 1/5(x^2+16)^{5/2} -16/3(x^2+16)^{1/2}+C $$ Homework Equations x=atanθ The Attempt at a Solution Mod note: The integral is ##\int x^3 \sqrt{x^2 + 16} dx## The published answer is ##1/5(x^2+16)^{5/2}...
  20. Dethrone

    MHB How can the integration limit be determined for a continuous function?

    Suppose $f$ is a continuous function on $(-\infty,\infty)$. Calculating the following in terms of $f$. $$\lim_{{x}\to{0}}f\left(\int_{0}^{\int_{0}^{x}f(y) \,dy} f(t)\,dt\right)$$
  21. T

    Constant of Integration in Trigonometric Substitution?

    Homework Statement So, I have a trigonometric substitution integration problem. The working is rather hairy, but I've gotten to the point where you draw the triangle to express theta in terms of x. But that's where I'm stuck! I think I may be having trouble with the constant of integration...
  22. R

    Trajectory of a turning particle

    In this problem, I need to find the trajectory of a particle (as a function of time) which moves at a speed 's' but also turns at an increasing rate; angular acceleration α. The trajectory looks like a spiral which converges to a point. The particle has an initial position vector p and a...
  23. C

    Integration using inverse trig indentities?

    Homework Statement 1.\int{\frac{sinx}{1+cos^{2}x}} \, dx 2.\int{\frac{1}{13-4x+x^2}} \, dx Homework Equations Inverse trig identities. The Attempt at a Solution For the first one, I'm not too sure about what to do with the sinx on the numerator and i have tried u-substitution to no avail...
  24. Aristotle

    Uniformly Charge on a Wire - Electric Field

    Homework Statement (Just for number 1 only - finding electric field) [/B] Homework Equations dE = k dq/R^2 sin theta = y/R = y / sqrt (a^2 + y^2) dq= lamda*dy The Attempt at a Solution [/B] I'm confused at the point of calculating the integral from -L/2 to L/2. I got the final integral...
  25. L

    Relation between integration and differentiation?

    relation between integration and differentiation ? how is instantaneous slope(differentiation) related to area under the curve(integration) ? thank you!
  26. V

    Integration of an arc of charge

    Homework Statement Two arcs of charge are center at the origin. The arc at radius r has a linear charge density of +(lambda) while the arc of radius 2r has a linear charge density of -(lambda). (r = 5cm, lambda = 1nC/m, theta = 40°) a) Calculate the magnitude and direction (as an angle from...
  27. Peeter

    Integration by parts, changing vector to moment & divergence

    In Jackson's 'classical electrodynamics' he re-expresses a volume integral of a vector in terms of a moment like divergence: \begin{align}\int \mathbf{J} d^3 x = - \int \mathbf{x} ( \boldsymbol{\nabla} \cdot \mathbf{J} ) d^3 x\end{align} He calls this change "integration by parts". If this...
  28. N

    Integration Regions: Convex and Continuous?

    Homework Statement What type of region(s) do the following classify as? Homework EquationsThe Attempt at a Solution I would classify D1 as both types; my reasoning is that by the definition of a convex polygon (i.e. all x,y in D1, the lie segment connecting x and y is entirely in D1), this...
  29. U

    Integrating a Definite Integral with Trigonometric Functions

    Homework Statement ∫dt/(t^2 +2tcos a + 1) (Limits of the integral are from 0 to 1) (0<a<π) Homework EquationsThe Attempt at a Solution Put t=sin a dt=cosa da ∫dt/(t^2 +2tcos a + 1) = ∫cos a da/(sin^2 a + sin 2a + 1) [ limits of integration changed to 0 to π/2] = ((cosec a)/2) ∫sin 2a da/(sin^2...
  30. J

    Integration in Laplace Transform

    Hello everyone, I have a question about integrating in Laplace Transform. For example, if I have: f(t)=e^{i.t} I have to solve this equation: \int_{0}^{\infty}e^{i.t}.e^{-s.t}dt If I do like this, it's very simple...
  31. E

    Integration of an acceleration formula involving vectors

    Homework Statement Suppose a constant force F acts on a particle of mass m initially at rest. (a) Integrate the formula for acceleration \vec{a} = \frac{\vec F}{\gamma m} - \frac{\vec v}{\gamma mc^2}(\vec F \cdot \vec v) where \gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} to show that the speed...
  32. N

    Integrating x^3 (x^2+20)^1/2: Steps & Answer

    Homework Statement the integral of x^3 (x^2 + 20)^1/2 Homework Equations use u substitution The Attempt at a Solution I think I have finally figured the problem out, can you confirm if this is the correct answer please? u=x^2 +20 x= sqrt(u-20) du= 2x dx integral of x^3 * sqrt( u) du/2x...
  33. thegreengineer

    Integral calculus: integral variable substitution confusion

    Recently I started seeing integral calculus and right now we are covering the topic of the antiderivative. At first sign it was not very difficult, until we started seeing integral variable substitution. The problem starts right here: Let's suppose that we have a function like this: \int...
  34. Calpalned

    Calculating Arc Length for Parametric Equation x = e^t + e^-t and y = 5 - 2t

    Homework Statement The question involves finding the arc length of the parametric equation x = e^t + e^-t and y = 5 - 2t Homework Equations Arc length of a parametric equation ∫√(dy/dt)^2 + (dx/dt)^2 dt limits are from 0<t<3 The Attempt at a Solution Taking the derivative of both x and y...
  35. Calpalned

    Use of integration to find area

    Homework Statement Find the area enclosed by the curve x = t^2 -2t, y = t^0.5 and the y axis Homework Equations Area of a parametric curve = ∫g(t) f'(t) dt, where g(t) = y and f(t) = x The Attempt at a Solution I believe that the limits of integration by be found by setting x and y equal to...
  36. C

    How Do I Match Integrals to the Correct Formulas in Integral Tables?

    I would really appreciate it if people could help with these integrals. We are supposed to be doing integrals with this table here: http://math.boisestate.edu/~wright/courses/m333/IntegralTablesStewart.pdf Here are the two integrals. Technically, I only need one of them completed...
  37. ognik

    Tricky Intregral for numerical quadrature

    Hi - I have just started 'Computational Physics' by Koonin & Meredith, - through distance learning. Exercise 1.3 needs a program to evaluate an integral - I'm finding myself kinda rusty on integrals. The hint says - split range of integration into parts, use different change of variable in each...
  38. A

    Just started Antiderivatives Help?

    Homework Statement F[/B]ind the Antiderivative of: (x^3-1)/(x-1). All is known is the integration formulas (i.e. ∫sinx = -cosx+c) Homework Equations Integration Formulas the most complicated being ∫cscx dx= -ln(cscx+cotx)+c The Attempt at a Solution I tried doing (x^3/x-1) -(1/x-1), but now...
  39. H

    Relationships between integration limits of Maxwell Equation

    I don't understand the relationships between the integration limits of Maxwell Equations (specifically the ones in integral form in matter) Is this related to Stokes/Gauss' Theorems? or something else?
  40. Mr Davis 97

    Defining differentitation and integration on functions

    I have a question concerning how how we define the differentiation and integration operators. Firstly, I know that functions are typically defined as an ordered triple triple ##(X, Y, f)## such that ##f⊆X×Y##, where ##x \in X## and ##f(x) \in Y##. This all seems nice and fine, but we also define...
  41. J

    MHB Integration by Parts for Cosine Squared: Is My Approach Correct?

    Greetings :) Well I wanted to seek help if my solution is on the right path, given as follows: 1) \int cos ^2x dx So my solution follows like this: u = cos^2x du = 1/2 (1+cos(2x)) v = x dv = dx but I've stuck when its in the u.v - \int v.du cos^2 (x) - \int...
  42. S

    Parametric + analytic function integration

    Hello. Let's imagine that we have a parametric function f1(x(t),y(t),z(t)) and an analytic one f2(x,y,z) and we have to integrate their product over some volume dx dy dz. So what are analytical tools for it? Thanks!
  43. A

    Residue of f(z) involving digamma function

    Homework Statement Find the residue of: $$f(z) = \frac{(\psi(-z) + \gamma)}{(z+1)(z+2)^3} \space \text{at} \space z=n$$ Where $n$ is every positive integer because those $n$ are the poles of $f(z)$Homework EquationsThe Attempt at a Solution This is a simple pole, however: $$\lim_{z \to n}...
  44. S

    Negative Volume of Revolution?

    There is a nice equation made by Nobuo Yamamoto which describes the curve of an egg and it is: (x^2 + y^2)^2 = ax^3 + (3/10)xy^2, where a is the length of the major axis of the egg. Solve this equation for y, we get: y=+/- sqrt((3/20)ax - x^2 + xsqrt((7/10)ax + (9/400)a^2)) When I rotate the...
  45. B

    Please explain how this integration is done

    Hi Attached is an extract of a paper by Lord Rayleigh on pressure generated during collapse of a bubble in a liquid. Will someone please explain how the RHS of equation (2) in the attachment is obtained ? TIA
  46. A

    MHB Replacing Variables in Integration

    I have asked the same question on math stackexchange under the moniker "anonymous," since I do not wish to be known there. I will try my luck here.$$I = \int_{-\infty}^{\infty} e^{-x^2} dx$$ I don't understand, we say: $$I = \int_{-\infty}^{\infty} e^{-x^2} dx$$ Then we say: $$I =...
  47. A

    Replacing Variables in Integration

    Homework Statement $$I = \int_{-\infty}^{\infty} e^{-x^2} dx$$ Homework Equations Below The Attempt at a Solution $$I = \int_{-\infty}^{\infty} e^{-x^2} dx$$ I don't understand, we say: $$I = \int_{-\infty}^{\infty} e^{-x^2} dx$$ Then we say: $$I = \int_{-\infty}^{\infty} e^{-t^2} dt$$...
  48. electronic engineer

    Integrate f(t) from 0 to 1/n: Explained

    Hello, I passed by this integration and couldn't understand the moving from the left hand to the right hand side. $$ \int_{0}^{1/n}f(t)dt=\frac{1}{n}f(0) $$ could you please tell me why this is??
  49. 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...
  50. 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...
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