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. solarmidnightrose

    B Understanding Kinematics in Calculus for High School Students

    hi, I'm a high-school student that is just beginning to learn calculus. in calculus we are learning how to apply integration and diffrentiaiton methods regarding kinematics. there is this certain phrase i do not really understand in our textbook: e.g."in the second second" how am i meant to...
  2. N

    Electrical Potential and an Integration path

    I have been looking everywhere for a clear explanation for the following: How do I know which way to integrate the electrical field, when I'm looking for the potential between to points? Example: I have to find the potential between the top conducting plate and the bottom conducting plate...
  3. Safder Aree

    Contour Integration over Square, Complex Anaylsis

    Homework Statement Show that $$\int_C e^zdz = 0$$ Let C be the perimeter of the square with vertices at the points z = 0, z = 1, z = 1 +i and z = i. Homework Equations $$z = x + iy$$ The Attempt at a Solution I know that if a function is analytic/holomorphic on a domain and the contour lies...
  4. D

    I Integration of the gradient of a vector

    Hi. Is it true to say that the integral over all volume of ∇ψ where ψ is a scalar function of position and time is just ψ ? Thanks
  5. J

    Problem with Complex contour integration

    Homework Statement I want to compute ##I=\int_C \dfrac{e^{i \pi z^2}}{sin(\pi z)}##, where C is the path in the attached figure (See below). I want to compute this by converting the integral to one whose integration variable is real.Homework Equations There are not more relevant equations. The...
  6. S

    How Do You Correctly Apply Integration by Parts to ∫-e^(2x)*sin(e^x) dx?

    Homework Statement I want to integrate ∫-e^(2x)*sin(e^x) dx Homework Equations ∫uv'dx=uv - ∫u'v The Attempt at a Solution u = e^2x du = 2*e^2x dv = sin(e^x) v = -cos(e^x)/e^x e^(x)*cos(e^x) - 2∫e^(x)*cos(e^x) dx e^(x)*cos(e^x) - 2*sin(e^x) + c The solution I have doesn't have the two in...
  7. A

    Integration help on physics problem

    Homework Statement Homework Equations F=ma F/m = a The Attempt at a Solution Fc = constant force fquad= cv'^2 [/B] (Fc-cv'^2)/m = a (Fc-cv'^2)/m = dv' / dt' * using the primes to differentiate between v and v' during integration dt '(Fc-cv'^2) dv'*(m) dt' = (m/ (Fc-cv'^2)) dv' dt'...
  8. D

    I Order of integration and taking limits

    Hi. I came across the following integral in contour integration lim(ε→0) "integral of" exp(iaεeiθ) dθ = θ If I take the limit first then it just becomes the integral of 1 which is θ. I have 2 questions - If I take the limit first and then perform the integral do I always get the same answer as...
  9. ys98

    I Can You Integrate Unit Vector ρ Without Switching to Cartesian Coordinates?

    When doing integration such as \int_{0}^{2\pi} \hat{\rho} d\phi which would give us 2\pi \hat{\rho} , must we decompose \hat{ρ} into sin(\phi) \hat{i} + cos(\phi) \hat{j} , then \int_{0}^{2\pi} (sin(\phi) \hat{i} + cos(\phi)\hat{j}) d\phi , which would give us 0 instead? Thanks
  10. 9

    I Integrating Discrete Data for Navigation: A Comprehensive Guide

    I have values for the variables (C, v, g, w at all sample points) but I do not know how to evaluate the integral. This equation is supposed to be implemented on a computer as part of a larger algorithm for navigation purposes. I have a feeling that the gyroscope sensor reading and or the...
  11. D

    Integration of Spherical Harmonics with a Gaussian (QM)

    Homework Statement I wish to solve this integral $$b_{lm}(k) = \frac{1}{2(\hbar)^{9/4}(2\pi)^{5/2}\sqrt{\sigma_{px} \sigma_{py} \sigma_{pz}}} \int_{\theta_k = 0}^{\pi}\int_{\varphi_k = 0}^{2\pi} i^l \text{exp}\left[ - \frac{1}{(2\hbar)^2}\left(\frac{(k_z - k_{z0})^2}{\sigma_{pz}^2} + \frac{(k_y...
  12. Philip Robotic

    Integration that leads to logarithm functions problem

    Hi everyone, So I am a high school student and I am learning calculus by myself right now (pretty new to that stuff still). Currently I am working through some problems where integration leads to logarithm functions. While doing one of the exercises I noticed one thing I don't understand. I...
  13. E

    Python Numerical Integration in Python

    I want to find the numerical solution to the following nested integral in Python \frac{K!}{(K-M)!}\int_{x_1=0}^{y}\int_{x_{2}=x_1}^{\max(x_1,\,y-x_1)}\cdots \int_{x_M=x_{M-1}}^{\max(x_{M-1},\,y-\sum_{m=1}^{M-1}x_m)} \frac{1}{(1+x_M)^{K-M+2}}\prod_{m=1}^{M-1}...
  14. navneet9431

    B What Is the Harm in Using Finite dx in Calculus?

    What does the author want to say through these lines? What is the *harm* he is talking about? I will be thankful for any help!
  15. D

    Contour integration around a square

    Homework Statement I am trying to calculate the contour integral of the complex conjugate of z around a square with sides of length 2 centred on the origin in the complex plane Homework Equations ∫ f(z) dz = ∫ f(t) (dz/dt) dt . It looks like the integral signs won't appear here but...
  16. Krushnaraj Pandya

    Integration problem (algebraic+trigonometric function)

    Homework Statement find integral of the function- (x^2 + cos^2)(cosec^2) / (1+x^2) 2. The attempt at a solution I noticed the denominator is the derivative of Arctan(x), I tried integrating by parts with various choices for 1st and second function but all of them end up being more complicated...
  17. Krushnaraj Pandya

    Integration problem ∫1/(√3 sinx+ cosx) dx

    Homework Statement ∫1/(√3 sinx+ cosx) dx is Ans. as per textbook 1/2(log(tan((x/2)+(pi/12)) 2. The attempt at a solution Attempt 1-I changed it to half angles (x/2) and then multiplied and divided sec^2(x/2) to the numerator and denominator, then putting tan(x/2)=t I got 2∫1/(√3t+1-t^2) I wrote...
  18. Krushnaraj Pandya

    Integration problem ∫sqroot((cosx-cos^3(x))/(1-cos^3(x)))

    Homework Statement Find ∫sqroot((cosx-cos^3(x))/(1-cos^3(x))) 2. The attempt at a solution I tried taking cosx common on top which gives cosxsin^2(x), but it didn't give me any benefit, I tried splitting the numerator, factoring in sec^2(x) and a bunch of substitutions to no avail. Finally...
  19. Krushnaraj Pandya

    Limits and integration problem

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  20. Krushnaraj Pandya

    What is the Fundamental Period of a Function with a Given Derivative?

    Homework Statement If the derivative of f(x) w.r.t x is (0.5- sin^2x)/f(x) then fundamental period of f(x) is 2. The attempt at a solution I wrote 1/2-sin^2x as cos2x/2. since f'(x)=cos2x/2f(x) its integral will be f(x), I would be grateful is someone could provide intuition on how to proceed...
  21. Krushnaraj Pandya

    What is the primitive of sinx/cos^2x?

    Homework Statement ∫e^(-x)(1-tanx)secx dx 2. Attempt at a solution I know ∫e^x(f(x)+f'(x))=e^x f(x) and I intuitively know f(x) could be secx here and therefore f'(x) will be secxtanx but I can't figure out how to reach that
  22. Krushnaraj Pandya

    How to Solve Basic Integration Problems Using Substitution and Partial Fractions

    Homework Statement ∫(√x)^5/((√x)^7+x^6) dx Homework Equations I have learned integration through substitution, trigonometric identities and standard integrals The Attempt at a Solution I took (√x)^5 common which gave 1/(x+√x^7), Then I tried to substitute √x=t, √x^7=t but it just seems to...
  23. Krushnaraj Pandya

    Conceptual integration question

    Homework Statement The value of ∫{[x]}dx (where {} and [] denotes the fractional part of x and greatest integer function) 1) 0 2) 1 3) 2 4)all are correct 2. The attempt at a solution Since [x] is always an integer, the given function will always have a value=0. I thought that since the...
  24. binbagsss

    Integrating Rational Functions with Substitution

    Homework Statement Apologies if this is obvious, maybe I'm a little out of touch ## \int\limits^b_0 \frac{x^3}{x^2+m^2} dx ## Homework EquationsThe Attempt at a Solution I [/B]was going to go by parts breaking the ##x^3 = x^2 . x## So that I have the logarithm I.e : ##b^2 \frac{log (b^2...
  25. SamRoss

    B Relativistic Energy: Change of Consts. of Integration

    In this super short video of the derivation of the relativistic kinetic energy, , I'm just stuck on one thing. Around 1:00 minute in, the constants of integration change from 0 to pv when the integration changes from dx to dv. Where does the pv come from? Thanks!
  26. George Keeling

    I Help with integration conventions in "Spacetime and Geometry" by Sean Carroll

    I am reading Spacetime and Geometry by Sean Carroll. In section 1.10 on classical field theory, he uses this formula (1.132) The curly L is a Lagrange density. S is an action, Φ is a vector potential. Could the integral also be written as follows?
  27. S

    Can dx/dy always be used for integration and derivation on a circle?

    Homework Statement is dx/dy= x/y if yes can i use it always Homework Equations for example in a circle dA/dtheta=A/360The Attempt at a Solution if its right sometimes what are the conditions of using it
  28. Prof Sabi

    Integration of an exponential function

    How to Integrate it::: ∫e^(ax²+bx+c)dx Or in general e raised to quadratic or any polynomial. I am trying hard to recall but I couldn't recall this integration. I tried using By-parts but the integration goes on and on.
  29. E

    First order perturbation energy correction to H-like atom

    Homework Statement Real atomic nuclei are not point charges, but can be approximated as a spherical distribution with radius ##R##, giving the potential $$ \phi(r) = \begin{cases} \frac{Ze}{R}(\frac{3}{2}-\frac{1}{2}\frac{r^2}{R^2}) &\quad r<R\\ \frac{Ze}{r} &\quad r>R \\...
  30. Mr Davis 97

    I Changing the limits of integration, getting 0

    I have the integral ##\displaystyle \int_0^{2 \pi} \frac{1-\cos x}{3+\cos x} ~ dx##. I want to make the tangent half-angle substitution ##t = \tan (x/2)## so that I can get a rational function. However, both limits of integration just become zero. This is the first case. In the second case, I...
  31. C

    I Integration - Projectile Motion w/ Air Resistance

    I"ve seen several texts that say something like this: Our equation of motion along x is dvx/dt = -g(vx/vt) Integrating this, we obtain equation 178 at this link (pretty near the top; sorry, but I can't figure out how to put the equation here). It's from FitzPatrick's online notes for...
  32. dRic2

    MATLAB What Does the Final Equation Represent in a Chemical Distillation Column?

    Here's what I have to do: 1) I arbitrary give a first value to the variable ##x_b##. Let's say ##x^{(0)}_b = 0.3## 2) I find ##x_D## by evaluating this integral: $$ln(\frac {52.32} {100}) = \int_{0.5}^{x^{(0)}_b} \frac {dx} {x^{(0)}_D - x}$$ 3) I use the value I got for ## x^{(0)}_D## to...
  33. M

    B Integration Basics: Uses & Benefits

    Where is it useful?
  34. E

    MATLAB What does a maximum number of intervals warning mean in numerical integration?

    Hi, I am trying to evaluate the following integral numerically in MATLAB \int_0^{\infty}\frac{e^{-jt}E_1^2(-jt)}{t}\,dt where ##j=\sqrt{-1}##, and ##E_1(x)## is the exponential integral. My code is fun = @(x) (exp(-1i*x).*(expint(-1i*x)).^2)./x; q = integral(fun,0,Inf) but I get the...
  35. Habib_hasan

    B How integration can find the summation of infinitely many rectangles?

    In definite Integration simply we find out the area under the curve.If I am not wrong the processing is like that we divide the area in infinite numbers of rectangles and then find out the summation of all rectangles area. My Question is here, how it is possible to add infinity? assume you have...
  36. A

    Calc 2 Integration Area Problem

    Homework Statement Please help me solve the calc problem pictured! Homework Equations y=3-x^2 and y=x+1 The Attempt at a Solution My attempt is in one of the photos!
  37. A

    Finding the limits of integration and quadratic formula

    Homework Statement Please look at the photo! Homework Equations -x^2+4x=x^2-6x+5 The Attempt at a Solution I got 2x^2-10x+5 but it says it's wrong
  38. gibberingmouther

    I How to derive this log related integration formula?

    here is a link with the formula: https://portal.uea.ac.uk/documents/6207125/8199714/steps+into+calculus+integration+and+natural+logarithms.pdf i'm talking about the formula that says the integral of f'(x)/f(x)dx = ln(f(x))+C it's kind of hard to put this into Google. where does this formula...
  39. E

    I Analyzing an Integral Solution for Exponential Integral with Imaginary Numbers

    Hello, Is this integral solvable in compact form? \int_0^{\infty}e^{-j\nu\alpha}E_1^m(-j\nu)\,d\nu where ##E_1(.)## is the exponential integral and ##j=\sqrt{-1}##. I am trying to avoid solving it numerically because its solution won't be the end result. Thanks
  40. E

    MATLAB How Can I Perform Double Numerical Integration in MATLAB or Mathematica?

    I have the pdf of a random variable found from the characteristic function given by f_X(\alpha)=\frac{1}{2\pi}\sum_{m=0}^Mj^m{K\choose m}\int_0^{\infty}e^{-jt(m+\alpha)}E_1^m(-jt)\,dt where ##j=\sqrt{-1}## and ##E_1(x)## is the exponential integral. I need to find the CDF of the random...
  41. R

    MHB Integration Basics: Axioms & Answers

    One of my students ask me: "Which axioms are the basic of the integration?" What I should answer him? Any ideas?
  42. donaldparida

    B Methods of integration: direct and indirect substitution

    I have seen two approaches to the method of integration by substitution (in two different books). On searching the internet i came to know that Approach I is known as the method of integration by direct substitution whereas Approach II is known as the method of integration by indirect...
  43. S

    Numerical integration of sharply peaking functions

    Homework Statement ∫ e1000((sinx)/x) dx [0 to 1000 : bound of integration]. Solve this integral of a sharply peaked function without a calculator. Homework Equations I'm doing this in relation to statistical thermodynamics - I think I need to use Sterling's Approximation or a gamma function...
  44. E

    Why Does Multiplying by 20 Correct My Monte Carlo Integration Result?

    Homework Statement $$f(x)=NormalPDF(x,2,1)+NormalPDF(x,2,(1/2)^2)$$. where NormalPDF(a,b) is the PDF for a normal distribution with mean a and variance b. Use Monte Carlo Integratoion to find: $$\int_{-10}^{10}f(x)dx$$ Homework Equations The solution to this integration is 2. I use the method...
  45. T

    A simple case of translation invariance of Riemann integrals

    Homework Statement Show that \int_{A} 1 = \int_{T(A)} 1 given A is an arbitrary region in R^n (not necessarily a rectangle) and T is a translation in R^n. Homework Equations Normally we find Riemann integrals by creating a rectangle R that includes A and set the function to be zero when x...
  46. M

    Why do I have to use integration and components?

    Homework Statement in the picture. Homework Equations F=ILcrossB Along with the original question, the other picture contains the solution with different numbers. I was just wondering why when finding the force on the wire instead of making dl= R*dtheta and going through the integration and...
  47. A

    A Conductivity and Integration over Fermi-Sphere?

    Hi, I am reading "An Introduction of Solid State Physics" from Ibach Lüth and don't understand the integration process. They write $$\sigma=\frac{e^2}{8\pi^3 \hbar} \int df_{E}dE \frac{v^2_x(\bf{k})}{v(\bf{k})} \tau(\bf{k}) \delta(E-E_F) $$ $$ = \int_{E=E_F}^{}df_{E}...
  48. binbagsss

    Integrating with Substitution: Clarifying the Contour and Chain Rule

    Homework Statement Homework Equations below The Attempt at a Solution I have shown that the first identity holds true. Because this is true without it being surrounded by an integral I guess you would need to integrate it all around the same contour ##C##. So say I have: ## _C \int...
  49. C

    Order of multi-variable integration of infinite range

    Homework Statement If the Green's function of the electric field in a system is G(x,x')=e^{-i(x-x')^2} I want to calculate the phase of the electric field at x if the source is uniformly distributed at x'=-\infty to x'=\infty Homework EquationsThe Attempt at a Solution Then, the phase of...
  50. T

    Integrating Gravitational Attraction in n Dimensions

    Homework Statement I'm working on a generalization of gravitation to n dimensions. I'm trying to compute gravitational attraction experienced by a point mass y due to a uniform mass distribution throughout a ball of radius a -- B(0, a). Homework Equations 3. The Attempt at a Solution [/B]...
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