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. 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 !
  2. 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) -...
  3. 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...
  4. 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...
  5. 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 ?
  6. S

    Python 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...
  7. 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...
  8. 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...
  9. 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...
  10. 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...
  11. 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...
  12. 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...
  13. 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...
  14. 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...
  15. 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?
  16. 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...
  17. kupid

    MHB Calculus & Diff. Eqn: Beginner Qs on Function, Derivative & Gradient

    I have some beginner doubts about Calculus and Differential equations . Is a function always a curve ? Doesn't a function already has a slope ? d/dx of a function gives the gradient of the curve between two points ? The derivative ,d/dx ,The gradient , is the rate of change of a...
  18. J

    A Analytical Integration of a Difficult Function

    Is it possible to integrate the following function analytically? ##\int_{0}^{\infty} \frac{\exp{-(\frac{A}{\tau}+B\tau+\frac{A}{\beta-\tau})}}{\sqrt{\tau(\beta-\tau)}}d\tau,## where ##A##, ##B## and ##\beta## are real numbers. What sort of coordinate transformation makes the integral bounded...
  19. S

    Integration with hyperbolic secant

    Homework Statement Solve ##\displaystyle{d\sigma = \frac{d\rho}{\cosh\rho}.}## Homework Equations The Attempt at a Solution The answer is ##\displaystyle{\sigma = 2 \tan^{-1}\text{sinh}(\rho/2)}##. See equation (10.2) in page 102 of the lecture notes in...
  20. Sarah00

    Integration. Where is the mistake? (if there is)

    Homework Statement Homework EquationsThe Attempt at a Solution My Solution: My Friend Solution: Are we both right? If not, who is right? and what is the mistake in other's solution! Thanks![/B]
  21. M

    I Find total charge (using double integration)

    The question asks to find total charge in a region given x has lower bound 0 - upper bound 5 , y has lower bound as 2 and upper bound as 5. Based on knowledge I have been reading throughout the chapter, I set up a double integration with those dxdy, but the results went out to be off - compared...
  22. binbagsss

    I Does dP_x dP_y = d^2\vec P : Integration scalar / vector var

    Excuse me if this is a bad question but: Does ##d P_x d P_y = d^2 \vec P ##? I thought not because ##P_x ## is a scalar , a component of the vector, whereas ##\vec P ## is a vector? Thanks in advance
  23. F

    I Integral involving square and log

    I have this integral that when solved, involves squares and natural logs, where ##A\,##,##\,b\,##, and ##\,x_e\,## are constants while ##x## is a variable. ##A = \int_{x_e}^{x} \frac{x^2 - b^2}{x} dx = \int_{x_e}^{x} x \, dx -b^2 \int_{x_e}^{x} \frac{dx}{x} = \frac{x^2}{2} - \frac{x_e^2}{2} -...
  24. davidge

    I Integrals: Why Change from M to $\phi(M)$?

    Yes, I know that I have already created another thread on this subject before. But, in this one, I would like to ask specifically why should we change from ##M## to ##\phi (M)## in the integral below? $$ \int_M (\partial_\nu w_\mu - \partial_\mu w_\nu) \ dx^\nu \wedge dx^\mu = \int_{\phi (M)}...
  25. X

    I Integration over something with addition in denominator

    Hi, I'm struggling to figure out how to do integration with forms such as: ∫ x/(x+1) dx ∫ x/(x+1)^2 dx ∫(b-x)^2/(b-a) dx This last one especially is giving me a strange issue, where if I plug it into wolfram: https://www.wolframalpha.com/input/?i=integrate+(b+-+x)%5E2+%2F(b-a)++dx It shows...
  26. D

    Integration of Thermodynamics equation w=–∫vDP

    Homework Statement Integrate w=–∫vDP from 2 to 1 and get k(P2V2-P1V1/1-k) The equation is used for steady flow, reversible and Ideal gas Homework EquationsThe Attempt at a Solution I'm not sure how to get the result
  27. doktorwho

    How to Prove the Integral Property for Definite Integrals

    Homework Statement Today i had a test on definite integrals which i failed. The test paper was given to us so we can practise at home and prepare better for the next one. This is the first problem which i need your help in solving:: Homework Equations 3. The Attempt at a Solution [/B] As no...
  28. B

    Calculus Books to learn integration techniques ?

    Are there books that are solely devoted to solving integrals and different methods in solving them ? I like solving integrals and I want to learn different techniques to solve integrals.
  29. binbagsss

    Cts approximation, delta function integration, stat mech

    Homework Statement Homework EquationsThe Attempt at a Solution So cts approx holds because ##\frac{E}{\bar{h}\omega}>>1## So ##\sum\limits^{\infty}_{n=0}\delta(E-(n+1/2)\bar{h} \omega) \approx \int\limits^{\infty}_{0} dx \delta(E-(x+1/2)\bar{h}\omega) ## Now if I do a substitution...
  30. Helmholtzerton

    MATLAB Filter out constant of integration?

    Hello, I'm trying to integrate a signal received on an oscilliscope, but I'm afraid using the function cumtrapz is not giving me the correct value. Here is what I'm seeing when testing out sine functions I could apply an FFt to obtain the components and the phases, and then subtract off the...
  31. F

    Complex integration on a given path

    Homework Statement Calculate the following integrals on the given paths. Why does the choice of path change/not change each of the results? (a) f(z) = exp(z) on i. the upper half of the unit circle. ii. the line segment from − 1 to 1. Homework Equations ∫γf(z) = ∫f(γ(t))γ'(t)dt, with the...
  32. P

    Verify orthogonality integral by direct integration

    This is a heat equation related math problem. 1. Homework Statement The complete question is: Verify the orthogonality integral by direct integration. It will be necessary to use the equation that defines the λ_n: κ*λ_n*cos(λ_n*a) + h*sin(λ_n*a)=0. Homework Equations κ*λ_n*cos(λ_n*a) +...
  33. S

    Density & Integration.... Help?

    Homework Statement A hole in the ground in the shape of an inverted cone is 19 meters deep and has radius at the top of 16 meters. The cone is filled to the top with sawdust. The density of the sawdust depends upon the depth, x, following the formula ρ(x) = 2.1 + 1.2e^(-1.2x) kg/m^3. Find the...
  34. Macykc2

    Can I Use Antiderivatives to Evaluate this Complex Integral?

    Homework Statement I need to evaluate the following integral using the antiderivative: $$\int log^2(z) \, dz$$ I don't know how to make a subscript for the integral sign, there should be a "c" on the bottom part. C is any contour from ##π## to ##i##, not crossing the non-positive x-axis...
  35. Unteroffizier

    How is gravitational acceleration affected with distance?

    Note: I didn't really know where to put this. It isn't a specific problem, but I've been asked by my physics teacher, who decided to give me and a few others an individual physics course of sorts, to find the means of solving similar problems. It's the first problem he assigned us, since we're...
  36. H

    Explanation for integration of Dr/Dt

    Homework Statement Why integration of $$\frac{D^2\mathbf r}{Dt^2}=−2\mathbf w \times \frac{D\mathbf r}{Dt}−g\mathbf R$$ gives us $$\frac{D\mathbf r}{Dt}= \mathbf v_0 −2\mathbf w×(\mathbf r−\mathbf r_0)−gt\mathbf R$$ Homework Equations Consider a time-varying vector written in the body...
  37. C

    I Limits of integration on Polar curves

    General question, how do you determine the limits of integration of a polar curve? Always found this somewhat confusing and can't seem to find a decent explanation on the internet.
  38. K

    B Applying L'Hospital's rule to Integration as the limit of a sum

    The definite integral of a function ##f(x)## from ##a## to ##b## as the limit of a sum is: $$\int_a^bf(x)dx=\lim_{h\rightarrow 0}h(f(a)+f(a+h)+.. ..+f(a+(n-2)h)+f(a+(n-1)h))$$ where ##h=\frac{b-a}{n}##. So, replacing ##h## with ##\frac{b-a}{n}## gives: $$\lim_{n\rightarrow...
  39. karush

    MHB Integration By Parts: uv-Substitution - 9.2

    $\tiny{9.2}$ \begin{align*} \displaystyle I&=\int y^3e^{-9y} \, dx\\ \textit{uv substitution}\\ u&=y^3\therefore \frac{1}{3}du=y^2dx\\ dv&=e^{-9y}\, dx\therefore v=e^{-9y}\\ \end{align*} will stop there this looks like tabular method better
  40. Demystifier

    I Error in Lorentz Invariant Integration

    Let ##j^{\mu}(x)## be a Lorentz 4-vector field in Minkowski spacetime and let ##\Sigma## be a 3-dimensional spacelike hypersurface with constant time of some Lorentz frame. From those I can construct the quantity $$Q=\int_{\Sigma} dS_{\mu}j^{\mu}$$ where $$dS_{\mu}=d^3x n_{\mu}$$ and ##n_{\mu}##...
  41. mercenarycor

    Contour integration with a branch cut

    Homework Statement ∫-11 dx/(√(1-x2)(a+bx)) a>b>0 Homework Equations f(z0)=(1/2πi)∫f(z)dz/(z-z0) The Attempt at a Solution I have absolutely no idea what I'm doing. I'm taking Mathematical Methods, and this chapter is making absolutely no sense to me. I understand enough to tell I'm supposed...
  42. Conductivity

    B Integration by Substitution Using Infinite Sums

    I have seen the wikipedia's proof which can be found here: https://proofwiki.org/wiki/Integration_by_Substitution However sometimes, we have problems where you have a ##d(x)## times ## f(g(x))## times g prime of x where we use substitution and it works but the proof didn't prove this...
  43. doktorwho

    Integration by substitution question

    Homework Statement Question: To solve the integral ##\int \frac{1}{\sqrt{x^2-4}} \,dx## on an interval ##I=(2,+\infty)##, can we use the substitution ##x=\operatorname {arcsint}##? Explain Homework Equations 3. The Attempt at a Solution [/B] This is my reasoning, the function ##\operatorname...
  44. K

    B Is the theory of fractional-ordered calculus flawed?

    Let's talk about the function ##f(x)=x^n##. It's derivative of ##k^{th}## order can be expressed by the formula: $$\frac{d^k}{dx^k}=\frac{n!}{(n-k)!}x^{n-k}$$ Similarly, the ##k^{th}## integral (integral operator applied ##k## times) can be expressed as: $$\frac{n!}{(n+k)!}x^{n+k}$$ According...
  45. E

    I Question about integration in physics

    I've always thought of integration as a way to solve differential questions. I'd solve physics problems involving calculus by finding the change in the function df(x) when I increment the independent variable (say x of f(x)) by an infinitesimal amount dx, attaching some physical significance to...
  46. K

    B Average angle made by a curve with the ##x-axis##

    The average angle made by a curve ##f(x)## between ##x=a## and ##x=b## is: $$\alpha=\frac{\int_a^b\tan^{-1}{(f'(x))}}{b-a}$$ I don't think there should be any questions on that. Since ##f'(x)## is the value of ##\tan{\theta}## at every point, so ##tan^{-1}{(f'(x))}##, should be the angle made by...
  47. EthanVandals

    Integration by Parts Twice: How to Solve Tricky Integrals

    Homework Statement Integrate e^3x sin x. Homework Equations uv - Integral(v du) The Attempt at a Solution I am trying to help somebody else with this problem, as I took Calculus a few years ago, but the end is really kicking my butt. I know I'm VERY close, but once I get to the second...
  48. Jovy

    Integrate $$y= \frac 1 {\sqrt{2\pi}}e^{ \frac{- x^2} 2},~y=0,~x=0,~x=1$$

    Homework Statement [/B] $$y= \frac 1 {\sqrt{2\pi}}e^{ \frac{- x^2} 2},~y=0,~x=0,~x=1$$ Homework Equations $$Volume=2\pi\int_a^b p(x)h(x)dx$$ The Attempt at a Solution I understand how to do the problem, I'm just having trouble integrating. ##h(x)=\frac 1 {\sqrt{2\pi}}e^{ \frac{- x^2} 2},~...
  49. E

    Why is the integral of a(x) different from the integral of a(t)?

    Hello! First time poster, please treat me well! :wink: I've already solved the problem below on my second attempt with the help of kinetic energy but I want to know why my first attempt gives a wrong answer. 1. Homework Statement A force in the +x-direction with magnitude F(x) = 18.0 N -...
  50. M

    I How Do I Symbolically Evaluate a Double Integral with an Offset Circle?

    Hello, I am new to the forum and need some help understanding how to evaluate this integral symbolically. ∫∫ r dA The differential element lies within a circle that is offset from the y-axis by some value R2, and the radius of the circle is R1. Again, the circle center location is (0,R2)...
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