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. U

    Light-like Geodesic - What are the limits of integration?

    Homework Statement Consider the following geodesic of a massless particle where ##\alpha## is a constant: \dot r = \frac{\alpha}{a(t)^2} c^2 \dot t^2 = \frac{\alpha^2}{a^2(t)} Homework EquationsThe Attempt at a Solution Part (a) c \frac{dt}{d\lambda} = \frac{\alpha}{a} a dt =...
  2. CAH

    Does integration give area between graph and x axis?

    Does integrating find the area between the curve and x-axis (regarless of it being a smile/frown or any other graph)? I've heard people say its the area UNDER a curve... but then how would you even get a definit answer surely it may be infinite if there's no restrictions? Thanks
  3. Yam

    Concept of Moment of Inertia and its limits of integration

    Homework Statement I am trying to work the moment of inertia for a) rotating rod, axis through the centre of the rod http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html#irod3 b) Solid cylinder http://hyperphysics.phy-astr.gsu.edu/hbase/icyl.html#icyl2 [/B] Homework Equations I = R^2 dM The...
  4. R

    MHB Integration Properties: Get Help with Parts B & C

    Please help me with this question. Part a was good but I don't understand parts b or c. Thanks in advanced.
  5. G

    My calculator's integration seems wrong

    This is the integral: http://www.wolframalpha.com/input/?i=integrate+x%5E2%2Bxy%2F2+from+0+to+x+with+respect+to+y But my calculator (TI-nspire cx CAS) gets this: x*(2x^2+xy)/2 Any idea why this is?
  6. K

    Calculating Distance Traveled on a Winding Trajectory From North to South Pole

    Homework Statement An airplane flies from the North Pole to the South Pole, following a winding trajectory. Place the center of the Earth at the origin of your coordinate system, and align the south-to-north axis of the Earth with your z axis. The pilot’s trajectory can then be described as...
  7. mooncrater

    Definite integration and stuff

    Homework Statement The question says: f (x)=x2+7x +∫0x(e-tf (x-t)dt. Find f (x). Homework Equations None The Attempt at a Solution What I did is: Consider the integral: I=∫0x (e-tf (x-t)dt We know that ∫abf (x)dx=∫abf (a+b-x)dc So using it here: 1/ex∫0xetf (t)dt----(1) Leaving the "1/ex...
  8. Alex_Neof

    How to determine the limits for triple integration?

    Homework Statement Evaluate the triple integral: ∫ x dxdydz A where A = {(x; y; z) : x, y, z > 0, x + y + z ≤ 1} . Homework Equations None that I know of. The Attempt at a Solution The problem I have is determining the limits for x, y and z. I don't really understand the following...
  9. karush

    MHB Integration by Parts with Domain Warning

    $\int x\ \cot^2\left({x}\right) dx $ $u=x$ $dv=\cot^2\left({x}\right) dx $ $du=\frac{x^2}{2}$ $v=\frac{-\cos\left({x}\right)+x\sin\left({x}\right)}{\sin\left({x}\right)}$
  10. Emmanuel_Euler

    Integration and special functions.

    what is the relationship between special functions and integration ? why integral of some function like (sqrt(ln(x)) and (cos(1/x) and more) are entering us to special functions?? PLEASE HELP ME TO UNDERSTAND.
  11. darida

    Integration of Ricci Scalar Over Surface

    Does this integration of Ricci scalar over surface apply in general or just for compact surfaces? ∫RdS = χ(g) where χ(g) is Euler characteristic. And could anybody give me some good references to prove the formula?
  12. AdityaDev

    Integration using substitution

    Homework Statement $$\int\frac{x^2+3}{x^6(x^2+1)}dx$$ Homework Equations None The Attempt at a Solution I easily got the answer using partial fractions by splitting the integral as ##\frac{Ax+B}{x^2+1}+\frac{C}{x}+\frac{D}{x^2}+\frac{E}{x^3}+...+\frac{H}{x^6}## and then finding the...
  13. chimath35

    Monte Carlo Integration for ∫ xdx/(2+3x)^2 with Bounds of 0 and 1

    Homework Statement Perform a Monte Carlo integration of: ∫ xdx/(2+3x)^2 with the bounds of 0 and 1 on the integral You should use 10 trials of at least 100 data pairs per trial and average the result I guess I am supposed to generate a x and y random number between 0 and 100 and if the...
  14. C

    Infinitesimals as interval limits in integration

    Ok so what I want to know is, is this valid? If so what does it mean?
  15. kostoglotov

    An equation for the path that the shark will swim on

    Homework Statement [/B] A shark will in the direction of the most rapidly increasing concentration of blood in water. Suppose a shark is at a point x_0,y_0 when it first detects blood in the water. Find an equation for the path that the shark will follow by setting up and solving a...
  16. ognik

    Confirm the equation for Numerov Integration method

    Homework Statement I am given the wave eqtn: (\frac {d^2} {dr^2}+\frac{1} {r} \frac {d} {dr})\Phi(r)=−k^2\Phi(r) The problems asks to 'show that the substitution $$ \Phi=r^{-\frac{1} {2}} \phi $$ gives an eqtn for which the Numerov algorithm is suitable'. Homework EquationsThe Attempt at a...
  17. Hepth

    Integration : Mapping Smoothly (-inf, 2] to [0.1,0.9]

    I have an Integral that is convergent over the range (-inf, Lambda) where 0< Lambda < 1. I need to change variables to move this to (0.1, 0.9) in such a way that I do not introduce any poor behavior, such as asymptotes or discontinuities as it needs to be well behaved. Is there a standard...
  18. B

    Diffrential equations, integration factor with two vars

    1. I need to find a condition that the equation will have a integration factor from the shape K(x*y). (K-integration factor sign) 2.the eq from the shape M(x,y)dx+N(x,y)dy=0 ,not have to be exact!3. i tried to open from the basics. d(k(x*y)M(x,y))/dy=d((k(x*y)N(x,y))/dx. and i used the fact...
  19. 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
  20. 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.
  21. 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
  22. 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...
  23. 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...
  24. 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...
  25. 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...
  26. 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...
  27. 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...
  28. AdityaDev

    How to Simplify the Integral of (sinx-cosx)ln(sinx) from 0 to π/2?

    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...
  29. 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...
  30. 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!
  31. 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...
  32. 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...
  33. 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.
  34. T

    Is ln(x-2) the Correct 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]
  35. 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...
  36. 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 ?
  37. 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}...
  38. 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 $f$. $$\lim_{{x}\to{0}}f\left(\int_{0}^{\int_{0}^{x}f(y) \,dy} f(t)\,dt\right)$$
  39. 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...
  40. 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...
  41. 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...
  42. 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...
  43. 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!
  44. 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...
  45. 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...
  46. 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...
  47. 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...
  48. 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...
  49. 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...
  50. 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...
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