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. Gliese123

    Why is cos(t)(cos(wt) - jsin(wt)) considered negligible in integration?

    Homework Statement Hi, I'm having a problem comprehending the odd-even trigonometry properties when doing an integration and I hope someone here feel like explaining since I can't seem to find anything of this in my course literature. I suppose it's more or less of a integration problem. f(t)...
  2. P

    Integration by substitution for sin/cos products

    Ok so I might be doing something silly but I just don't understand what is going on here. So the integral: i = ∫ sin x (cos x)^3 dx First I say u = cos x. So du = - sin x dx. So now I have i = ∫ - u^3 du. Which gives: i = -(1/4)u^4 or -(1/4)(cos x)^4. Easy. But if I say u = sin x...
  3. A

    Need help using substitution before integration

    Hi I just started calc 2 and am stuck on a problem. integral ln(x+x^2)dx. They want to use substitution prior to integrate by parts, but I'm completely stuck. Can anyone help explain how to solve?
  4. G

    How can the integral of a complex function be simplified?

    Homework Statement \int sin e^{-x}+e^x cos e^{-x}\,dx Find the integral above Homework Equations The Attempt at a Solution I tried substituting u=e^{-x}, but i get \int \frac{sin u}{u}+\frac{cos u}{u^2} \,du, which is non-integrable function.
  5. Dethrone

    MHB Integration with trig and hyperbolic substitutions

    Suppose we want to find: $$\int \frac{1}{\sqrt{x^2-a^2}}\,dx$$ Trig Substitution: $$=\ln \left| x+\sqrt{x^2-a^2} \right|$$ Hyperbolic Substitution: $$=\cosh^{-1}\left({\frac{x}{a}}\right)=\ln\left({x+\sqrt{x^2-a^2}}\right)$$ I know this is super minor, but how are they equivalent when one...
  6. Dethrone

    MHB Integration - Find all functions f(x)

    Find all functions $f(x)$ so that $\left(\int \frac{dx}{f(x)}\right)\left(\int f(x) \,dx\right)=c$, constant. The question says "no guessing". I looked at families of functions, starting with $f(x)=a$, $f(x)=x^n$, and $f(x)=\sin\left({x}\right)$, but they all fail. Any hints? (Wondering)
  7. J

    MHB How to Calculate the Indefinite Integral of a Complex Function?

    Calculation of $\displaystyle \int \frac{\sqrt[4]{x^{10}+x^8+1}}{x^6}\cdot \left(3x^{10}+2x^{8}-2\right)dx$ $\bf{My\; Try::} $ Given $\displaystyle \int \frac{\sqrt[4]{x^{10}+x^8+1}}{x^6}\cdot \left(3x^{10}+2x^{8}-2\right)dx = \int\frac{\sqrt{x^6+x^4+x^{-4}}}{x^5}\cdot...
  8. A

    Traditional integration of X^3

    Hi, I'm trying to prove that the integral of x^3 (x cubed) between the limits of a (lower limit) and b (upper limit) is: (b^4)/4 - (a^4)/4 I'm using the traditional method of dividing the area into n rectangles (where n tends to infinity). Hence the width of 1 rectangle is (b-a)/n...
  9. S

    Integration involving continuous random variable

    Homework Statement please refer to the question, i can't figure out which part i did wrongly. i 'd been looking at this repeatedly , yet i can't find my mistake. thanks for the help! the correct ans is below the question. where the c= 283/5700 , q = 179/5700 Homework Equations The...
  10. Dethrone

    MHB Absolute values in Integration

    I feel like I'm asking the weirdest questions that most people don't ask, but here it is. Suppose we have this integral (I made it up): $$\int \sqrt{x^4+2x^3+x^2}$$ Now, I feel most people would say the answer is simply, $\frac{1}{3}x^3+\frac{1}{2}x^2+C$. But technically, that is only true...
  11. C

    Multivariable Calculus - Integration Assignment 1#

    Homework Statement Evaluate the integral, \iiint_E z dzdydz Where E is bounded by, y = 0 z = 0 x + y = 2 y^2 + z^2 = 1 in the first octant.Homework Equations Rearranging y^2 + z^2 = 1 it terms of z , z = \sqrt{1-y^2} The Attempt at a Solution From the given equations I...
  12. C

    Multivariable Calculus - Integration Assignment

    Homework Statement Here is my assignment, http://imgur.com/1edJ3g5 I figured it would be easier if we know we are both looking at the same thing! I'm looking for help with question 2. I seem to be having trouble with the integration. Homework Equations r=acosθ x^2 + y^2 + z^2 = a^2...
  13. C

    Multivariable Calculus - Integration Assignment

    Homework Statement Hello PF! I'm having some trouble on the last part of my assignment, it's question 4 part "c". Here is a picture of the assignment [http://imgur.com/1edJ3g5] ! I'll post this instead of writing it out so we know that we're all looking at the same thing!Homework Equations The...
  14. gfd43tg

    Adaptive step size trapezoidal integration

    https://www.physicsforums.com/attachments/72086 https://www.physicsforums.com/attachment.php?attachmentid=72087&d=1407804589 Hello Here is the code for the adaptive stepsize function function I = arttrap(fh,a,b,tol,fa,fb) if nargin == 4 fa = fh(a); fb = fh(b); end m = (a+b)/2; fm = fh(m)...
  15. Dethrone

    MHB Did I make a mistake in this integral?

    I'm really exhausted mentally, so it'll be really helpful if someone can tell me where I made a mistake. I'm rotating surfaces, and with that, I had to solve this integral: $$=\pi \int \sqrt{64-3x^2} dx$$ $$=\frac{\pi}{\sqrt{3}} \int \sqrt{\frac{64}{3}-x^2} dx$$ Let $$x = \frac{8}{\sqrt{3}}...
  16. B

    Integrating Discrete Spaces and Time: Implications for Continuum and Precision

    We know that in order to be integrated a function must be continuous. Does this imply that space and time must be a continuum? If they were considered discrete, say at the level of Planck's unit, would this affect the integrability of functions? It it would not, would it affect the precision...
  17. M

    MHB Definite Integration of a concave upward function- Inequality

  18. K

    Integration of 6-12 Lennard Jones Potential to obtain the 3-9 one.

    Hi people, I'm researching about the interactions of two carbon atoms using the Lennard-Jones potential and I need to know the theory behind some equations. I need to know how to get from the 6-12 potential the 3-9 one. I've found in this link (...
  19. kartikwat

    Changing the function w.r.t in integration

    How to change the function w.r.t we are doing integration(function other then x) .what does it mean to do so.
  20. NaughtyBear

    Possible integration techniques for laptop keyboards

    Hello there! I am attempting to use a laptop keyboard I just salvaged from a spare. I noticed the laptop keyboard has a ribbon connection. Further research has told me that the ribbon cable essentially just sents signals to a processor attached to the motherboard. In other words, I cannot use it...
  21. M

    Integration by trigonometric change of variable

    Homework Statement I'm trying to solve ##\int\sqrt{a^2 - x^2}## by using the substitution ##x = asin\theta## Homework Equations ##x = asin\theta The Attempt at a Solution ##y = \int\sqrt{a^2 - a^2cos^2\theta}## ##y = a\int\cos\theta## ##y = a^2\int\cos(\theta)^2## ##y = (a^2)/2 *...
  22. A

    Calculus Beyond Integration: What's Next?

    This question may sound simplistic but is there a mathematical process which lies directly beyond integration integration, or more specifically beyond finding the antiderivative? And by that I mean loosely what is the next step? I do apologize if this statement sounds vague to higher minds. But...
  23. E

    Solving Integration Problems | Get Expert Help Now

    Hey! I have this integral: ∫((1/2)/(2x-1))dx. The first time, I did like this: ∫((1/2)/(2x-1))dx = (1/2)∫(1/(2x-1))dx. If I set u = 2x-1, then du = 2dx, so I can rewrite (1/2)∫(1/(2x-1))dx as (1/2)*(1/2)∫(1/u)du = 1/4∫(1/u)du = 1/4ln|u| = 1/4ln|2x-1|. But when I do like this (I cannot...
  24. M

    Integration using residue theorem (part 2)

    Hello. I need some explanation here. I got the solution but I don't understand something. Question: Find the integral using Residue Theorem. $$\int_{-\infty}^{\infty}\frac{dx}{(x^2+4)^2}$$ Here is the first part of the solution that I don't understand: To evaluate...
  25. A

    MHB Integration using residue theorem (part 2)

    Hello. I need some explanation here. I got the solution but I don't understand something. Question: Find the integral using Residue Theorem. $$\int_{-\infty}^{\infty}\frac{dx}{(x^2+4)^2}$$ Here is the first part of the solution that I don't understand: To evaluate...
  26. Mogarrr

    Integration Problem: Showing Integral Equals 1

    Homework Statement I'm trying to show that the definite integral: \int_0^{\infty} \frac 1{\sqrt{2 \pi}} \sqrt {y} e^{\frac {-y}2} dy , equals 1. Homework Equations it's already known that \int_0^{\infty}\frac 1{\sqrt{2 \pi}} y^{\frac {-1}2} e^{\frac {-y}2} dy = 1 , since f(x) is...
  27. Greg Bernhardt

    What is Integration By Parts? A 5 Minute Introduction

    Continue reading...
  28. M

    Integration using residue theorem

    Hi. I have to use the residue theorem to integrate f(z). Can someone help me out? I am stuck on the factorization part. Find the integral $$\int_{0}^{2\pi} \,\frac{d\theta}{25-24\cos\left({\theta}\right)}$$ My answer: $$\int_{0}^{2\pi}...
  29. A

    MHB Integration using residue theorem

    Hi. I have to use the residue theorem to integrate f(z). Can someone help me out? I am stuck on the factorization part. Find the integral $$\int_{0}^{2\pi} \,\frac{d\theta}{25-24\cos\left({\theta}\right)}$$ My answer: $$\int_{0}^{2\pi}...
  30. Dethrone

    Understanding integration with trig identities, and absolute value

    Homework Statement In integration, we are allowed to use identities such as sinx = \sqrt{1-cos^2x}. Why does that work, and why doesn't make a difference in integration? Graphing \sqrt{1-cos^2x} is only equal to sinx on certain intervals such as(0, \pi) and (2\pi, 3\pi). More correctly...
  31. Dethrone

    MHB Integration with trig identities and absolute value

    In integration, we are allowed to use identities such as sinx = \sqrt{1-cos^2x}. Why does that work, and why doesn't make a difference in integration? Graphing \sqrt{1-cos^2x} is only equal to sinx on certain intervals such as (0, \pi) and (2\pi, 3\pi). More correctly, shouldn't we use the...
  32. E

    Partial Fractions - Integration

    Homework Statement Evaluate the integral. (Remember to use ln |u| where appropriate. Use C for the constant of integration.) \int \frac {5x^2 - 20x +45}{(2x+1)(x-2)^2}\, dx Homework Equations 5x^2 - 20x +45 = 5 (x^2 -4x +9) The Attempt at a Solution I'm able to come up with an...
  33. F

    MHB Contour Integration: Calculating the Integral of $1/z$ with Residue Formula

    Calculate the integral of $1/z$ around $C$, where $C$ is any contour going from $-\sqrt{3}+i$ to $-\sqrt{3}-i$ and is contained in the set of complex numbers whose real part is negative. My answer: Let $f=1/z$ Then $f$ has a simple pole at $z=0$ with residue 1. How do I calculate the winding...
  34. A

    MHB Calculus II Volumes of Revolution and Basic Integration Questions

    Hey guys, I have a couple of questions about the problem set I'm doing at the moment. Although I was able to solve most of these, I'm doubting quite a few of my responses. http://i.share.pho.to/f7d7efe6_o.pnghttp://i.share.pho.to/82c05629_o.png http://i.share.pho.to/d6f76bb6_o.png...
  35. I

    MHB Integration and population dynamics?

    can someone explain this problem step by step (not a homework problem, just an example i found and i want to see how its done). a hot wet summer is causing a mosquito population explosion in a lake resort area. the number of mosquitoes is increasing at an estimated rate of 2200+10e^(0.8t) per...
  36. S

    What did I do Wrong with this integration by u-sub

    Homework Statement ∫x^2(a^2-x^2)^.5 limits from 0 to a Homework Equations ∫x^2(a^2-x^2)^.5 limits from 0 to a The Attempt at a Solution It's way to much for me to type in the short amount of time I have so I included a picture of my work. It's neat and easy to read. the...
  37. E

    Integration by Parts Evaluate the integral

    Homework Statement Evaluate the integral. (Use C for the constant of integration.) ∫te ^ (-9t) dtHomework Equations ∫udv = uv - ∫vdu u=t dv= e ^ (-9t) dt du=dt v=(-1/9) e ^(-9t) The Attempt at a Solution = -1/9 te^(-9t) - ∫-1/9 e ^(-9t) dt Second Integral...
  38. A

    MHB Calculation of real integration

    Hi. Is there a short way to calculate real integration? I tried it but it looks so tedious. I attached the question so please refer to that. I am stuck with no.1, by the way. Here is my attempt: ∫_0^(2π) dx/(13 - 5*sin(x)) let u = tan(x/2) which means x/2 = arctan(u) which means x =...
  39. M

    Relationship integration math problem

    This is about attempting to solve ##\left( y'\right)^2 = y^2 - 1 ##. \int\frac{dy}{\sqrt{y^2 -1}} = \pm \int dx using a trig. substitution and another trick, \int\frac{dy}{\sqrt{y^2 -1}} = \ln\left(y \pm \sqrt{y^2 - 1} \right) + C I'm not sure about that \pm sign. It came in when doing \tan...
  40. E

    Why do we get oscillations in Euler's method of integration and what i

    When using Euler's method of integration, applied on a stochastic differential eq. : For example - given d/dt v=−γvΔt+sqrt(ϵ⋅Δt)Γ(t) we loop over v[n+1]=v[n]−γv[n]Δt+sqrt(ϵ⋅Δt)Γn. (where −γv[n] is a force term, can be any force and Γn is some gaussian distributed random variable. ) . Then if...
  41. I

    MHB Further applications of integration

    so i know I've asked this question before but id really like a step by step walk through with a few questions. starting with $\int_{\pi/3}^{\pi} \ \sqrt{1+\frac{4}{x^2}},dx$ i know I am not showing any work but id like to see how to this can properly be done. thanks wait never mind i think i...
  42. V

    How do the different concepts of integration fit together?

    I'm making this new post in the general math section since I don't know what field of math this question belongs to anymore. So the picture I currently have regarding the abstractions of integration and differentiation from single variable-calculus to multi-variable calculus is that the...
  43. I

    MHB How can I determine which integration technique to use for a specific problem?

    (Wave)I have a test tomorrow on the different Techniques of Integration: integration by parts, partial fractions, trigonometric integrals, trigonometric substitutions, improper integrals and i want to fully understand them. I've been working on problems from the book but can someone just give a...
  44. I

    MHB Integration by Parts: Solve $$\frac{xe^{2x}}{(1+2x)^2}$$

    Im supposed to use integration by parts for this problem but i understand how to. $$\int \ \frac{xe^{2x}}{(1+2x)^2},dx$$
  45. I

    MHB Integration Help: Solve in 3 Hours, Steps Included

    please help! this homework assignment is due in like 3 hours and i have to get it done. $$\int \frac{1 \, dx}{(x^2+8x+17)^{2}}$$ $$\int_{-1/ \sqrt{3}}^{1/ \sqrt{3}} \frac{e^{arctan {y}} \, dy}{(1+y^2)}$$ i need to see all the steps. do i use partial fractions for the first one?
  46. A

    Proof of integration power rule

    Hey, I was just wondering if there was a way to prove the power rule for integration using the definition of a definite integral. And I don't mean using the proof for the differentiation power rule, I mean is it possible to derive \displaystyle\large\int_a^b x^c=\frac{b^{c+1}-a^{c+1}} {c+1}...
  47. B

    Integration by Parts To Derive Expectation Value of Velocity

    Homework Statement Why can't you do integration-by-parts directly on the middle expression in equation 1.29--pull out the time derivative over onto x, note that \displaystyle \frac{\partial x}{\partial t} = 0, and conclude that \displaystyle \frac{d \langle x \rangle }{dt} = 0Homework Equations...
  48. V

    Abstractions of integration and differentiation

    I have a few questions about the generalizations of concepts like integration and differentiation of single-valued functions of a single variable to vector-valued functions of several variables. All in the context of real analysis. Beginning with scalar-valued functions of several variables...
  49. schrodingerscat11

    Electric field due to a spherical charged shell (direct integration)

    Homework Statement Find the electric field a distance z from the center of a spherical surface of radius R which carries a uniform density σ. Treat the case z<R (inside) as well as z>R (outside). Express the answers in terms of the total charge q on the sphere. Homework Equations E = \int...
  50. J

    Integration with hypergeometric function

    How to integrate: _{2}F_{1}(B;C;D;Ex^{2})\,Ax where _{2}F_{1}(...) is the hypergeometric function, x is the independent variable and A, B, C, D, and E are constants.
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