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. L

    Is Integration by Parts Incorrect for ∫(x2 + 7x) cosx dx?

    ∫(x2 + 7x) cosx dx If I make v = (x2 + 7x) and du = cosx dx I get ((x2 + 7x) sinx)/2 If I make v = cosx and du = (x2 + 7x) dx I get ((x3/3 + 7x2/2) cosx)/2 using the form X=Y-X to X=Y/2 Neither are correct, what did I do wrong?
  2. fluidistic

    Statistical mechanics, confused about an approximation and limits of integration

    Homework Statement Hello, I tried to solve a problem on my own and then I looked up a solution on the web, and I realize that it seems that I goofed. The problem statement can be found at http://www.hep.fsu.edu/~reina/courses/2012-2013/phy5524/homework/solutions/hw5_sol.pdf (Problem 1, part...
  3. N

    Can factorials be integrated in this equation?

    Hello, well here's my problem: I got this integral and I don't know how to calculate it (I am trying to find if there exists a k that satisfies this relation) : \int_0^k \frac{1}{ ( 4k-4r-2 ) ! ( 4r+1 ) ! }\, \left ( \frac{y}{x} \right )^{4r} dk = \int_0^k \frac{1}{ ( 4k-4r ) ! ( 4r+3 ) ! }\...
  4. M

    Integration of A exp( (− 3 R^2)/(2Na^2)) (whilst following forum rules; I think)

    Homework Statement A exp( (− 3 R^2)/(2Na^2)) I wish to integrate ^ The expression is equal to P(N,R) The limits are infinity to -infinity. The intention is to find the normalisation constant / A in terms of N and a (then to cube it).The Attempt at a Solution This is what I've managed. A S...
  5. M

    Integration of A exp( (− 3 R^2)/(2Na^2))

    Hi! Could someone please integrate the expression (with intention of finding the normalisation constant / value of A). Thanks a lot!
  6. S

    Tricky DeltaFunction integration

    Hey! There is a question. Here is the integral: What I'm trying to do is starting with the third integral over zi and with the help of integral definition of DeltaFunction i want to calculate it. As you can see f(yi) has no influence on the integral. Am i right here?
  7. N

    Confusion with integration of sums

    Hello guys, since I am new at sums and multivariable calculus I faced a problem when I stumbled upon this: \sum_{r=0}^{k} \binom{n}{4r+1} x^{n-4r-1} y^{4r+1} = \sum_{r=0}^{b} \binom{n}{4r+3} x^{n-4r-3} y^{4r+3} Well, the problem is that I don't know if it's possible to put a limit in every...
  8. PsychonautQQ

    Why are the results of this natural log integration seemingly inconsistent?

    Homework Statement Integrate (-m-kx)^-1 dx from a to b. The Attempt at a Solution So using the integral form I get the integral of (-m-kx)^-1 dx is (-1/k)*[ln(-m-kx)] with the bracketed expression being evaluated between a and b. (-1/k)*[ln(-m-ka) - ln(-m-kb)] My first...
  9. R

    Integration test of dirac delta function as a Fourier integral

    Homework Statement Problem: a) Find the Fourier transform of the Dirac delta function: δ(x) b) Transform back to real space, and plot the result, using a varying number of Fourier components (waves). c) test by integration, that the delta function represented by a Fourier integral integrates...
  10. L

    Volumes of Irregular Shapes by Integration

    Hi all, Is it possible to determine the volume of a shape where, in the x and y dimensions, the shape is described by an equation, and then its elevation is described by another equation? An example would be a parabola in the x-y plane whose elevation is based on another parabolic...
  11. Jadaav

    Integration involving complex exponentials

    Homework Statement \int[( e^x + 4 )/ (4e^x + 1) ]^2 Homework Equations No substitutions have been given. The Attempt at a Solution I've tried using the method of f' (x)/f (x). But it was in vain. I haven't been able to do it. I don't really know where to start.
  12. R

    Trig Integration By Substitution

    Mod note: Moved from technical math section ∫(2x+6)/sqrt(5-4x-x^2) I have 2/3(ln|tan(theta)+sec(theta)|-3|cos(theta)|) where x=sin^-1((x+2)/3)
  13. P

    Electrical potential inside a sphere using integration

    Homework Statement Find the electrical potential inside a spherical shell carrying a total charge Q by integrating over the surface.Homework Equations E=k q/r^2The Attempt at a Solution I know the answer is zero from Gauss's law, but I don't know how to do the integration to get it.
  14. C

    MHB Do you say this integration is doable?

    Hi I have an integral to do $$\nu =\int_{0}^{P(r)} \,\frac{dP}{P+\beta\rho(P)}$$ here I calculated $$\rho = 0.003 P^{\frac{2}{4}}+ 0.002P^{\frac{2.5}{4}}+0.0019P^{\frac{3}{4}}$$ My question can this integral be solved anyhow? I tried it in wolfram but it failed, can anyone give me the...
  15. A

    Changing limits of integration - definite integral (without u sub)?

    Hello Can someone please tell me how is: \int_{-R}^{R} \frac{\cos mx}{x^2 + 1}\,dx = 2\int_{0}^R \frac{\cos mx}{x^2 + 1}\,dx where, m and R are positive real numbers This is how I'm trying to solve it... \int_{-R}^R \frac{\cos mx}{x^2 + 1}\,dx = \int_{-R}^0 \frac{\cos mx}{x^2 + 1}\,dx...
  16. M

    Compute causal function using integration by parts

    Homework Statement I stuck on, when the question as for integration by parts method. Need advice
  17. B

    How to think about complex integration

    Let's say you integrate a complex function along a curve. How do you visualize it? This is explaned very well in multivariate calculus in terms of work, or for instance the weight of the line of we integrate over the density etc.. But when we look at complex function I get this: The function...
  18. 8

    Integration by Parts: Solve ∫cos(x)cos(kx)dx

    Homework Statement Hello! I am having some trouble solving this integral by parts. I hope someone can help me. ##\int \cos(x)cos(kx) dx## It is need for a Fourier seriesHomework Equations I am using this definition: ##\int f(x)g(x) dx = f(x)G(x)-\int f'(x)G(x) dx## since its an even...
  19. 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)...
  20. 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...
  21. 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?
  22. 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.
  23. 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...
  24. 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)
  25. 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...
  26. 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...
  27. 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...
  28. Dethrone

    MHB How Do Absolute Values Affect 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...
  29. 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...
  30. 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...
  31. 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...
  32. 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)...
  33. 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}}...
  34. 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...
  35. M

    MHB Definite Integration of a concave upward function- Inequality

  36. 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 (...
  37. 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.
  38. 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...
  39. 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 *...
  40. 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...
  41. 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...
  42. 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...
  43. 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...
  44. 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...
  45. Greg Bernhardt

    What is Integration By Parts? A 5 Minute Introduction

    Continue reading...
  46. 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}...
  47. 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}...
  48. 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...
  49. 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...
  50. 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...
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