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. L

    MHB Visualization of Integration by Parts

    Hello all, I am trying to understand the rational behind the visualization of integration by parts, however I struggle with it a wee bit. I was trying to read about it in Wiki, this is what I found...
  2. H

    Faraday's law with Calc 3 integration help

    Homework Statement Suppose an infinitely long wire carrying current ##I=sin_0(\omega t)## is a distance ##a## away from a equilateral triangular circuit with resistance ##R## in the same plane as shown in the figure. Each side of the circuit is length ##b##. I need to find the induced voltage...
  3. karush

    MHB 15.3.53 Sketch the region of the double integration and evaluate

    $\textsf{a. Sketch the region of integration and evaluate.}\\$ \begin{align*}\displaystyle \int_{6}^{\frac{\pi}{6}} \int_{0}^{\sec{\theta}} 6r^{3} drd\theta\\ W|A=\frac{5}{3\sqrt{3}} \end{align*} OK I really didn't know how to do this in desmos
  4. S

    I Understanding Integration on an Orientable Manifold

    Hello! I am reading how to integrate on an orientable manifold. So we have ##f:M \to R## and an m-form (m is the dimension of M): ##\omega = h(p)dx^1 \wedge ... \wedge dx^m##, where ##h(p)## is another function on the manifold which is always positive as the manifold is orientable. The way...
  5. C

    A Ikonal equation integration -- source code request

    Hi. I would like a source code to integrate the ikonal equation. I would like to compute the ray path. Of course I am able to compute the phase refractive index n(x,y). Cartesian system is preferred. Can anybody give me a suggestion? Bye, Carlos
  6. C

    Calculating Work with Vector Components and Variable Force

    Hello all! I usually don't like to ask for help... But this is the first week of courses and I'm already stumped on a homework question... 1. Homework Statement So the question states: Find the work by the force F = x^i + xy^j. If the object starts from the origin (0,0), moves along the...
  7. karush

    MHB 15.2.60 Reverse the order of integration

    $\textsf{Reverse the order of integration in the following integral }$ \begin{align*}\displaystyle I&=\int_0^1 \int_2^{2e^x}f(x,y) dydx \end{align*} ok tried to follow some examples but 😰 \begin{align*}\displaystyle I&=\int_0^1 \int_?^{?}f(x,y) dxdy \end{align*}
  8. karush

    MHB 15.2.66 Solve by reversing the reversing the order of integration

    solve by reversing the reversing the order of integration this was given: \begin{align*}\displaystyle I&=\int_0^8 \int_{\sqrt[3]{x}}^2 \left[\frac{x}{y^7+1}\right]dy \, dx\\ \end{align*} ok I put this in an dbl int calculor but it turned the order around to \begin{align*}\displaystyle...
  9. T

    B Simple double integration of square wave question

    Hi, Simple question, sort of: I see that according to the internet the mathematical description of a triangular wave is rather complex, so I'll try to stay as far away from that as I can, because I'm a bit rusty. I understand that if you integrate a square wave you get a triangular wave on the...
  10. S

    Is Neural Integration a Tangible Metric or Just Scientific Jargon?

    What does this mean, and is it true?
  11. F

    Work problem involving a variable force

    Homework Statement A CD case slides along a floor in the positive direction of an x-axis while an applied force Fa acts on the case. The force is directed along the x-axis and has the x component Fax = 7.0x – 2.0x^2, with x in meters and Fax in Newtons. The case starts at rest at the position x...
  12. D

    One-dimensional integration - flux

    <Moderator's note: Moved from a technical forum and thus no template.> Calculate flux of the vector field $$F=(-y, x, z^2)$$ through the tetraeder $$T(ABCD)$$ with the corner points $$A= (\frac{3}{2}, 0, 0), B= (0, \frac{\sqrt 3}{2},0), C = (0, -\frac{\sqrt 3}{2},0), D = (\frac{1}{2},0 , \sqrt...
  13. kelvin490

    MATLAB Solving equation with integration using MATLAB

    I would like to solve an equation below using MATLAB: All the parameters except p are known, so I only need to solve for p. However since I need to consider the sign of the integrand and there is an absolute value sign in it I don't know how to solve it. Could anyone please help? Thank you.
  14. Q

    Difficulties with Substitution Rule (integration)

    I can obviously do the chain rule and see how the final expression of the derivative is related to the original function but I can't seem to figure out the substitution Rule as an intuitive way of solving the indefinite integral of functions... bear with me if I'm too verbose, I've attached an...
  15. karush

    MHB W.8.8.19 Integration of 2 to \infty

    $\tiny{w.8.8.19}$ $\textsf{Integration of $2$ to $\infty$}$ $$\displaystyle I_{19} = \int_{2}^{\infty} \frac{\cos\left({\pi/x}\right)}{{x}^{2}}\,dx $$ $\textit{Not sure how to break this down but it appears the denominator will advance faster than the numerator}$
  16. M

    MHB Finding the Area of a Disc with Integration Methods

    Use integration methods to establish the formula A = π r^2 for the area of a disc ofradius r. so the equation of the circle is x^2 +y^2 =r^2 . i will try and find the area of one quadrant using integration. so it will be ∫ r,0 y dx so ∫ r,0 √(r^2 -x^2) dx so from here i am trying to integrate...
  17. maistral

    A Integration by parts of a differential

    I'll cut the long story short. What on Earth happened here: I seem to be unable to do the integration by parts of the first term. I end up with a lot of dx's.
  18. A

    B Why is integration with dx in the denominator undefined?

    Hello, In your opinion, why the integration with dx in the denominator is undefined ?? (as in the attached picture)
  19. F

    Using parameterisation to calculate work done by force

    A force F = -K(yi + xj) (K is a positive constant) acts on a particle moving in the x-y plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). What is the total work done by the force F on the...
  20. Mr Davis 97

    Integration by Parts with Logarithmic Functions

    Homework Statement ##\displaystyle \int \frac{\log (x)}{x}~ dx## Homework EquationsThe Attempt at a Solution I am a little confused about the first part. We know that the ##\displaystyle \int \frac{1}{x}~ dx = \log |x|##. So how can we proceed with integration by parts if one of the logs has...
  21. Saracen Rue

    Integration only giving one answer?

    Homework Statement If ##a>0## and ##b≠0##, solve the following stating the maximal domain for which the solution is valid: ##\sqrt{a^2-x^2}\cdot \frac{dy}{dx}+b=0,\ y\left(0\right)=0## Homework Equations [/B] ##\int _{ }^{ }\frac{1}{\sqrt{a^2-x^2}}dx=\arcsin \left(\frac{x}{a}\right)+c,\ a>0##...
  22. Mzzed

    Integration of multiple exponentials

    Homework Statement I am struggling with solving this integral that seems to look easy on the surface but integration isn't my strong suit and so I'm not 100% sure on how to go about solving this: ∫ (120(e-15.24t - e-39984.75t))2dt where the integration is from 0 to 0.3 Homework EquationsThe...
  23. M

    Legendre Polynomial Integration

    Homework Statement Simplify $$\int_{-1}^1\left( (1-x^2)P_i''-2xP'_i+2P_i\right)P_j\,dx$$ where ##P_i## is the ##i^{th}## Legendre Polynomial, a function of ##x##. Homework Equations The Attempt at a Solution Integration by parts is likely useful?? Also I know the Legendre Polynomials are...
  24. Adgorn

    I Question regarding integration of an equation

    I am beginning to learn about differential equations and I saw in an explanatory video a solution to this separable differential equation: ##\frac {dy} {dx} = \frac {-x} {y{e^{x^2}}}## from there through simple steps the equation changed to ##y⋅dy=-xe^{-x^2}⋅dx ##. Then the video did an...
  25. G

    B How to integrate a polar graph with respect to radius

    How is this done? My textbook only specifies integrating polar graphs with respect to theta.
  26. Ackbach

    MHB Data Science and Systems Integration Blog Post

    Really excited about this blog post by yours truly. Wineman Technology is going places!
  27. A

    How Can I Integrate with Dirac Delta in this Expression?

    Homework Statement I need to integrate this expression : P(k, w) = A * δ(w-k*v) * f(k, w) A is constant and δ, Dirac Delta.Homework Equations [/B] There is double integration : I = ∫0∞ dk ∫0∞ P(k,w) dw = A ∫∫0∞ δ(w-k*v) * f(k, w) dw dk The Attempt at a Solution [/B] I'm confused with...
  28. O

    I Confusion over using integration to find probability

    Hey everyone, first, let me say I understand the complement rule. Where I am confused is over the integration. My professor said that suppose you have a continuous cumulative distribution function F(x) = 1-e-x/10, if x > 0 (0, otherwise). And suppose you want to find P(X>12) you can use the...
  29. C

    I Integrate Over Domain? | General Integration Questions

    I have a question about integration and I hope I can word it correctly. When we integrate over something (i.e. a line, a surface, or volume), what exactly do I integrate over? Is it the domain of that "thing"? I feel like it's something I've been told but I just can't remember. If this is the...
  30. Alan Sammarone

    I Integration of Legendre Polynomials with different arguments

    Hi everybody, I'm trying to calculate this: $$\sum_{l=0}^{\infty} \int_{\Omega} d\theta' d\phi' \cos{\theta'} \sin{\theta'} P_l (\cos{\gamma})$$ where ##P_{l}## are the Legendre polynomials, ##\Omega## is the surface of a sphere of radius ##R##, and $$ \cos{\gamma} = \cos{\theta'}...
  31. T

    Integrate (sinx+cosx)/sqrt(1+sin2x)

    Homework Statement Integrate: (sinx + cosx)/sqrt(1+sin2x) Homework Equations Simple trigo formulae: cos2x=cos^2(x)--sin^2(x) sin^2(x)+cos^2(x)=1 sin2x=2.sinx.cosx The Attempt at a Solution I tried to rationalize the given term,multiplying both numerator and denominator with: 1st time:cosx-sinx...
  32. T

    Integrate 4cos(x/2)cos(x)sin(21x/2) Homework

    Homework Statement Integrate: 4cos(x/2).cos(x).sin(21x/2) Homework Equations ▪sin(A+B)=sinAcosB+sinBcosA ▪2sinAcosA=sin2A And obviously, ▪Integration of sinx is (-cosx) ▪Integration of cosx is (sinx) The Attempt at a Solution ○I multiplied the numerator and denominator with sin(x/2) ○The...
  33. T

    Integrate [(x^4+x^2+1)/2(1+x^2)]dx: Soln & Explanation

    Homework Statement Integrate: [(x^4+x^2+1)/2(1+x^2)]dx Homework Equations [/B] Integral of x^n=x^(n+1)/(n+1) Integral of 1/(1+x^2)=arctanx The Attempt at a Solution I have attached my solution.All the steps seem to be correct,but the answer isn't matching,don't know why.
  34. T

    Integrating [(x^2+3)/(x^8+x^6)] dx by Substitution

    Homework Statement Solve the following integral: [(x^2+3)/(x^8+x^6)] dx [/B] Homework Equations The question has also said to integrate by substitution(though other methods are welcome) That would mean substituting an expression in x with a variable,say, 't' such that the integral comes of...
  35. A

    Integration of an inverse polynomial

    Hello, I want to integrate this expression : ∫ (x5 + ax4 + bx3 + cx2 + dx)-1 between xmin>0 and xmax>0 a is positive but b, c and d can be positive or negative. I have no idea to integrate this expression... Do you have methods to do this ? Thanks in advance !
  36. J

    I Lorentzian line shape integration

    Hi, I know this might be a bit dum but I'm currently stuck with this integral. In this link: http://www.pci.tu-bs.de/aggericke/PC4e/Kap_III/Linienbreite.htm I know he's doing the right thing, but I really don't understand the integral of a(omega). How come it is E(1/(i(ω-ω0) -γ) -...
  37. Shakattack12

    Integration Applications Question

    Homework Statement Hi, the question just states find the area of the pink, within a square, without giving an equation for the pink boundary line. I did look up the formula for the lens shape but was wondering how to do this with integration. The area of the square is 1 un2. Sorry about the...
  38. J

    Analytic Integration of Function Containing the Exponential of an Exponential

    Homework Statement Can this function be integrated analytically? ##f=\exp \left(-\frac{e^{-2 \theta } \left(a \left(b^2 \left(e^{2 \theta }-1\right)^2 L^2+16\right)-32 \sqrt{a} e^{\theta }+16 e^{2 \theta }\right)}{b L^4}\right),## where ##a##, ##b## and ##L## are some real positive...
  39. G

    B Integration of a quantity when calculating Work

    While integrating work we write dw = INT. F.ds. But why can't we write dw = INT. dF.s ?
  40. S

    Numerical integration in Python (throwing a ball)

    Homework Statement I have a problem with my physics task, but you do not need to understand physics to be able to help me, because my main problem is bad programming skill. I am dealing with a problem of throwing a ball in the air at an angle between 0 an 45 degrees. I need to consider not only...
  41. S

    I Learning Complex Integration: Endpoints & Paths

    Hello! I started learning about complex analysis and I am a bit confused about integration. I understand that if we take different paths for the same function, the value on the integral is different, depending on the path. But if we use the antiderivative...
  42. E

    Integration method (Navier) calculating deflection

    Homework Statement A beam is given with a constant load. Calculate the deflection at the end of the beam. Use the integration method or method of navier with delta functions. Homework Equations See equations in my attached file. The Attempt at a Solution The red load you see on the drawing is...
  43. yecko

    Maximizing Integration Expansion | Homework Solution

    Homework Statement https://holland.pk/uptow/i4/d6adf6b4297ef9c8c20c3e58ec66535d.png Homework Equations integration The Attempt at a Solution [/B] https://holland.pk/uptow/i4/36ea9fcf0a17f1ea8137f0140c881289.jpg I have got stuck at this step... And have no idea on how to go on to the...
  44. H

    B Does integration commute with substitution t=0?

    Let ##g(x,t)=\int f(k,x,t)\,dk## Under what conditions is the following true? ##g(x,0)=\int f(k,x,0)\,dk## That is, we can get the value of ##g(x,t)## when ##t=0##, by (1) either substituting ##t=0## into ##g(x,t)## or (2) by first substituting ##t=0## into ##f(k,x,t)## and then integrating...
  45. binbagsss

    Integration question involving square root

    Homework Statement How to integrate ## \frac{dx}{dt}=\sqrt{\frac{k}{x}-1}## AND ## \frac{dx}{dt}=\sqrt{\frac{k}{x}+1}## k a constant here. I'm unsure what substitution to do. Many thanks in advance. Homework EquationsThe Attempt at a Solution I can't really get started as I'm unsure...
  46. R

    Can anyone explain this integration for me?

    Homework Statement http://imgur.com/a/Y8NW0 Basically we start with a function of t, which was differentiated twice, that function = F_o / m Fo is a constant force, and I assume m is mass though my book doesn't state that. Homework EquationsThe Attempt at a Solution Integrating the...
  47. H

    Calculating the equations of motion for particle in parabola

    I made the problem up myself, so there might very well not be a rational answer that I like! Homework Statement A point-particle is released at height h0 is released into a parabola. The position of the particle is given by (x, y) and the acceleration due to gravity is g. All forms of friction...
  48. J

    I Taylor expansions and integration.

    I have a short doubt: Let f(x) be a fuction that can't be integrated in an analytical way . Is anything wrong if I expand it in a Taylor' series around a point and use this expansion to get the value of the definite integral of the function around that point? Suppose that the interval between...
  49. harpazo

    MHB Integrating (x^2cosx^3)^6: A Review of Techniques

    Integrate this (x^2cosx^3)^6. I absolutely forgot how to integrate several calculus 2 integrals. Integration by parts? Substitution? Trig sub? Partial fraction decomposition?
  50. D

    Area between 2 curves, Volume around X and Y, Centroid

    g(x)= √(19x) = upper curve f(x)= 0.2x^2 = lower curve Firstly, I found the point of intersection, which would later give the upper values for x and y. x=7.802 y=12.174 Then I found the area under g(x) and took away the area under f(x) to get the area between the curves. 31.67 units^2 This is...
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