# 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. ### Integration problem using inscribed rectangles

Just went through this...steps pretty clear. I refreshed on Riemann integrals { sum of rectangles approximate area under curves}. My question is on the highlighted part in Red. The approximation of area under curve may be smaller or larger than the actual value. Thus the inequality may be ##<##...
2. ### change in the unit vectors

i tried integrating the stuff but it didn't work what to do
3. ### Partial fractions with complex linear terms

I am interested specifically in solving this problem by factoring the quadratic term into complex linear factors. $$s^2+4=0$$ $$\implies s=\pm 2i$$ $$\frac{5s+6}{(s-2i)(s+2i)(s-2)}=\frac{A}{s-2i}+\frac{B}{s+2i}+\frac{C}{s-2}$$ We can solve for ##C## using the cover-up method with ##s=2## to...

34. ### Impulse integration for a Tennis Racket hitting a Tennis Ball

For this, Can someone please tell me why they integrate the impulse over from ##t_i## to ##t_f##? Why not from ##j_i## to ##j_f##? It seems strange integrating impulse with respect to time. Many thanks!
35. ### B Explain Integration to me, please

Hi all, I understand what the integral does - it calculates the area under a curve and can easily see how it could be used to calculate an area of land. What I do not understand is really the physical meaning when it comes to the real world. Here are some examples: 1. A set of data...
36. ### Insights Can You Solve the Mathematical Mystery Behind the Art of Integration?

This article cannot replace the 1220 pages of the almanac Gradshteyn-Ryzhik but it tries on 1% of the pages to summarize the main techniques. Continue reading...
37. ### Solution to Schwarzschild Equation for Constant t,r

In 1916, Karl Schwarzschild was the first person to present a solution to Einstein's field equations. I am using a form of his equation that is presented in Tensors, Relativity and Cosmology by Mirjana Dalarsson and Nils Dalarsson (Chapter 19, p.205). I am approaching what may be the simplest...
38. ### Insights An Overview of Complex Differentiation and Integration

I want to shed some light on complex analysis without getting all the technical details in the way which are necessary for the precise treatments that can be found in many excellent standard textbooks. Analysis is about differentiation. Hence, complex differentiation will be my starting point...
39. ### I Integration of Bessel function products (J_1(x)^2/xdx)

Hello, While reading Sakurai (scattering theory/Eikonal approximation section), I encountered a referenced integral ## \int_0^\infty J_1(x)^2\frac{dx}{x}=1/2 ## I also see this integral from a few places (wolfram, DLMF, etc), so I tried to prove this from various angles (recurrence relations...
40. ### Symbolic integration of a Bessel function with a complex argument

Hello all I am trying to solve the following integral with Mathematica and I'm having some issues with it. where Jo is a Bessel Function of first kind and order 0. Notice that k is a complex number given by Where delta is a coefficient. Due to the complex arguments I'm integrating the...
41. ### I Parameter Integration of Bubble Integral

Referring to this link : https://qcdloop.fnal.gov/bubg.pdf Using Mathematica Integrate command to solve it does not give the result stated here but I am unclear as to how they got to the result in the 4th line. It is clear that the integrand (1st line) can diverge for certain values of the...
42. ### Applying integration to math problems

Ok i know that, ##\int (x+2)^2 dx= \int [x^2+4x+4] dx= \dfrac{x^3}{3}+2x^2+4x+c## when i use substitution; i.e letting ##u=x+2## i end up with; ##\int u^2 du= \dfrac{u^3}{3}+c=\dfrac {(x+2)^3}{3}+c=\dfrac{x^3+6x^2+12x+8}{3} +c## clearly the two solutions are not the same... appreciate your...
43. ### I Calculate Length Contraction for Accelerated Motion to Proxima Centauri

Let's assume a spaceship traveling from the Earth to the Proxima Centauri with constant acceleration g = 9.81 m/s2. The ship is accelerating the first half of the trajectory and decelerating the second half. I calculated the velocity profile from the Earth reference: The travel time on...
44. ### Question about approximate numerical integration methods

This isn't a homework question per se but I can post more details like the data points & my work after. Suppose we are given a set of arbitrary points for which we cannot find an equation and we need to find the area under the curve without an analytical method - we can use either of the three...
45. ### Confused about polar integrals and setting up bounds

So I want to subtract the two surfaces, right? I really don't know where to start... I am guessing this would be some sort of triple integral, however I am very confused with the bounds. Any help would be greatly appreciated! Thanks!!
46. ### I Relating integration of forms to Riemann integration

Partition each closed interval ##[a_i,b_i]## in the Cartesian product, ##A##. Denote the partition for the i-th closed interval as ##\{x_i^1,\ldots,x_i^{k_i}\}##. The Cartesian product of the partitions forms a partition of ##A## (think: a lattice of points that coincide with the points of each...
47. ### No Limits of Integration for Electric Field Integral?

For this problem, The solution is, However, why have they not included limits of integration? I think this is because all the small charge elements dq across the ring add up to Q. However, how would you solve this problem with limits of integration? Many thanks!
48. ### I Verifying Integration of ##\int_0^1 x^m \ln x \, \mathrm{d}x##

I'm trying to compute ##\int_0^1 x^m \ln x \, \mathrm{d}x##. I'm wondering if the bit about the application of L'Hopital's rule was ok. Can anyone check? Letting ##u = \ln x## and ##\mathrm{d}v = x^m##, we have ##\mathrm{d}u = \frac{1}{x}\mathrm{d}x ## and ##v = \frac{x^{m+1}}{m+1}##...
49. ### Find ##f(x)## in the problem involving integration

Q. 3(b). This is a textbook problem; unless i am missing something ...the textbook solution is wrong! solution; Mythoughts; ##f(x)=2\cos 3x-3\sin 3x## ...by using the product rule on ##\dfrac{d}{dx} (e^{2x} \cos 3x)##.
50. ### Integration of structure function F2 to calculate quark momentum

I study particle physics with “Particles and Nuclei” / Povh et al. and “Modern particle physics” / Mark Thomson and I am currently at “Deep-Inelastic scattering”. After introducing several scattering equations, such as Rosenbluth, that all include terms for electric AND magnetic scattering, i.e...