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. H

    Structural Dynamics Analysis - Modal method or time integration?

    Hi all, I need help with numerical solution of motion equation. From the numerical point of view and in the real of the finite element method, which method is recommended for the solution of damped ( proportional damping) linear motion equation? I have been trying three common methods; Modal...
  2. A

    Flow switch integration with piezo alarm

    Dear all, I am mechanical engineer with no background to circuitry and electronics. I am trying to connect a flow switch ( using hall effect ,12 dc input) and I want it to trigger a piezo alarm (12V dc) when water flow stops. There are three wires from the flow switch, two for power and...
  3. jdawg

    What kind of Integration to use

    Homework Statement ∫(x2)/(ex/2) dx Homework Equations The Attempt at a Solution I'm not completely sure where to start on this one. I don't see any sort of u substitution working, would integration by parts be a good idea? Maybe let u=x2 and dv=(1/ex/2) ?
  4. P

    Numerical integration using Weber force

    I need to compute numericaly n-body sys. interacting acording to the Weber force: http://en.wikipedia.org/wiki/Weber_electrodynamics and I have a problem with the acceleration on rhs: r'', because the acceleration is unknown, due to the Newton law: F = ma, and we need just 'a' to do next...
  5. J

    Closed integration of exact form

    If ##\omega## is an exact form ##( \omega = d\eta )## and ##\Omega## is the region of integration and ##\partial \Omega## represents the boundary of integration, so the following equation is correct: $$\\ \oint_{\partial \Omega} \omega = 0$$?
  6. S

    How do I do this integration using u sub?

    Homework Statement ∫x^2√(2+x) using u sub Homework Equations ∫x^2√(2+x) The Attempt at a Solution I can't seem to find anything to use for a u sub. if I sub 2+x I just get 1, and if I sub x^2 I just get 2x If I do √(2+x) I just get 1/2(1/√(2+x))
  7. Saitama

    MHB A very basic question about integration

    I encountered this when I tried to evaluate the following integral with help of complex numbers. $$\int_0^{\infty} \frac{dx}{x^2+1}$$ The answer is obviously $\pi/2$ as the integrand is derivative of $\arctan(x)$. Now, I tried it it using partial fraction decomposition: $$\int_0^{\infty}...
  8. J

    Integration - slightly confused

    Hi I'm trying to integrate the following q_m = -D A \frac{dc}{dx} where A = 4 \pi r^2 Yes, a sphere.My supplied literature simplifies to q_m = -D 2 \pi r L \frac{dc}{dr} when A = 2 \pi r L Integrating to \int_{r1}^{r2} q_m \frac{dr}{r} = - \int_{c1}^{c2} 2 \pi L D dc Integrated to q_m ln...
  9. DreamWeaver

    MHB A Dilogarithmic integration by parts

    From the logarithmic integral representation of the Dilogarithm, \text{Li}_2(x), |x| \le 1, prove the reflection formula for the Dilogarithm. Dilogarithm definition:\text{Li}_2(x) = -\int_0^1\frac{\log(1-xt)}{t}\, dt = \sum_{k=1}^{\infty}\frac{x^k}{k^2}Dilogarithm reflection...
  10. S

    How do I do this integration by substitution?

    Homework Statement ∫1/(3+((2x)^.5))dx the answer should be ((2x)^.5) - 3ln(3+((2x)^.5)) + c I keep getting ((2x)^.5) - ln(3+((2x)^.5)) + c Homework Equations ∫1/(3+((2x)^.5))dx The Attempt at a Solution I did: u = 3 + ((2x)^.5) du = 1/((2x)^.5) dx du((2x)^.5) = dx...
  11. H

    Integration by Parts and Series

    This isn't really a homework question, more just something I noticed while evaluating an integral and was curious about: At this stage, I was able to simplify the expression before solving for the integral algebraically (since the second iteration yielded the original integral the right...
  12. A

    MHB Complicated integration of complex number

    Hello. I am not confident about this question. I think I have to use cauchy integral formula. But before that, I should decompose the fraction, right? Or is there a simpler way to do it?　A friend told me that each contour only had one pole interior to it so he just used the Cauchy integral...
  13. M

    Complicated integration of complex number

    Hello. I am not confident about this question. I think I have to use cauchy integral formula. But before that, I should decompose the fraction, right? Or is there a simpler way to do it?　A friend told me that each contour only had one pole interior to it so he just used the Cauchy integral...
  14. A

    Area of a polygon- using numerical integration

    Hi, I need to calculate area of an irregular polygon which can be of any complex shape numerically i.e. using numerical integration techniques. Please can anyone suggest any reference material / best way of going about this efficiently? Akash
  15. Uday

    A Doubt Regarding Quantization of charge ,its relevance in integration

    a) We know that the smallest charge that can exist is 'e' . But in several instances (such as calculating potential energy of sphere of charge ) we consider 'dq' and then integrate it . How can we justify this ? b) We know that 1/2 or 1/3 of e (charge of electron) doesn't exist . But...
  16. T

    Numerical integration methods applicable to a type of definite integral

    Numerical integration methods applicable to a type of definite integrl Hey, so I've been working on a program to numerically integrate an integral of the form ∫xnf(x) dx, LIM(0 to INF.) Here n can go to negative non integral values, say -3.7 etc. and f(x) is a function of sin, cos and...
  17. P

    Integration by substitution: Can I treat this as constant

    I am trying to compute the following integral: \int \exp^{w^T \Lambda w}\, d\theta where \Lambda is a constant wrt \theta w = y - t(x, \theta) So, I am trying to use substitution and I have: d\theta = \frac{-dw}{t^{'}(x, \theta)} So, substituting it, I have the following integral...
  18. A

    Integration of x/(a^2+x^2)^2/3

    in this video , the prof had to integrate x/(a^2+x^2)^3/2 , i know we usually do this using substitution , but in the video...he ignored the x and integrate like it was 1/(a^2+x^2)^3/2, how does that work?
  19. H

    Integration of below expression

    Homework Statement it is capacitor charging expression..how to find its integration Homework Equations VL(t) = ∫_(T/2)^T▒〖Vme^(-T/2RC) 〗 dt The Attempt at a Solution result is 0.5...but how
  20. T

    Is this valid when doing u substitution for integration?

    So I'm doing length of an arc in my calculus 1 class. After plugging everything in the arc length formula. Now I have this complicated function to integrate. Square root of (16x^8+8x^4+1)/16x^4. I took the denominator out of my square root and got 4x^2. Now I take u=4x^2. Du/2x =dx...
  21. F

    Integration by Partial Fractions

    Homework Statement Find the indefinite integral of the below, using partial fractions. \frac{4x^2+6x-1}{(x+3)(2x^2-1)} Homework Equations ?The Attempt at a Solution First I want to say there is probably a much easier and quicker way to get around certain things I have done but I have just...
  22. G

    Unerstanding an Integration question

    Homework Statement for -1≤x≤1, F(x) =∫sqrt(1-t^2) from -1 to x ( sorry don't know how to put the limits on the sign a. What does F(1) represent geometrically? b. Evaluate F(1) c. Find F'(x) Homework Equations The Attempt at a Solution Since my teacher never seems to give...
  23. E

    How do you know when to use substituion or integration by parts?

    When you have a fraction, how do you know when to use iteration by parts, or use substituion, pick a u, solve for a value of x (like x=u-2) and then plug in those values?
  24. A

    MHB Complex Integration: Solving $\int_{|z|=1} |z-1|.|dz|$

    Can you check my work please, Compute $\displaystyle \int_{|z|=1} |z-1| . |dz| $ $ z(t) = e^{it} , 0 \leq t < 2 \pi $ $ |dz| =| ie^{it} dt | = dt $ $\displaystyle \int_{0}^{2\pi} |\cos(t) + i\sin(t) - 1 | dt $ $\displaystyle \int_{0}^{2 \pi} \sqrt{(\cos(t) -1)^2 + \sin ^2( t)} \, dt =...
  25. T

    Proof Involving Integration by Parts and a Series of Functions

    Homework Statement Let f be continuous on an interval I containing 0, and define f1(x) = ∫f(t)dt, f2(x) = ∫f1(t)dt, and in general, fn(x) = ∫fn-1(t)dt for n≥2. Show that fn+1(x) = ∫[(x-t)n/n!]f(t)dt for every n≥0. ALL INTEGRALS DEFINED FROM 0 to x (I can't format :( ) Homework...
  26. E

    Trig substitution integration?

    Homework Statement Integrate dx/((x^2+1)^2) Homework Equations Tan^2=sec^2-1 The Attempt at a Solution So I let x=tanx then dx=sec^2x Then plugging everything in; Sec^2(x)/(tan^2+1)^2 So it's sec^2/(sec^2x)^2) which is sec^2x/sec^4x Canceling out the sec^2 gives...
  27. F

    Should Integration by Parts Be Used on Functions Like \( x \cdot y(x) \)?

    Homework Statement I want to take an antiderivative of a function with respect to x. But in addition the function includes a term y (x) that is a function of x itself. Do I have to apply the reverse power rule also to y(x) also? The integral can be seen as an indefinite. Homework...
  28. Y

    Order of Integration: How to Change from dxdydz to dydxdz?

    1. The problem statement, all variables and given/known Show that ∫∫∫ 12y^2 z^3 sin[x^4] dxdydz Region: { y< x< z 0< y< z 0 <z< (Pi)^ 1/4 Equals Pi/4 Change order of integration to dydxdz 2. Homework Equations Order of integration 3. The Attempt at a...
  29. D

    Integration substiuition of new variable

    Homework Statement for this question, my ans is pi/2 not pi/4 . can anybody please check where's the mistake? Homework Equations The Attempt at a Solution
  30. U

    Integration by Parts Homework: Get Help Now

    Homework Statement Homework Equations N/A The Attempt at a Solution I can't even begin the attempt because I don't know how you could use intergration by parts for this sum in the first place. Can you help me out?
  31. D

    What is a suitable substitution for this integration problem?

    Homework Statement for this question, the question only stated SUITABLE substituition, what substituition should i use? this substituion does not involve trigo functions , am i right? P/S : I'm just asking opinion, not the full working. Homework Equations The Attempt at a Solution
  32. Digitalism

    Cone with spherical top triple integration

    Homework Statement Homework Equations ∫∫∫dV The Attempt at a Solution Ok so I started by setting my bounds equal to √(200-x^2-y^2) ≥ z ≥ √(x^2+y^2), √(100-x^2) ≥ y ≥ -√(100-x^2), 10 ≥ x ≥ -10 which I got from solving z^2 = (200-x^2-y^2) = x^2+y^2 => x^2+y^2 = 100 but it...
  33. D

    Seperate variable and integration

    Homework Statement for this Q and t are variables, 10 and surd k are constant, is my working correct? Homework Equations The Attempt at a Solution
  34. M

    Multivariable Calculus Triple Integration Problem

    Homework Statement Express the iterated integral ∫[0,1]∫[0,1-y^2]∫[0,y] f(x,y,z)dzdxdy a. as a triple integral (i.e., describe the region of integration); b. as an iterated integral in the order z, y, x; c. as an iterated integral in the order y, z, x: The Attempt at a Solution so...
  35. M

    Multivariable Double Integration Problem

    1. The problem statement Fill in the blanks ∫ [0,1] ∫ [2x^2,x+1] f(y) dy dx = ∫ [0,1] ( ) dy + ∫ [1,2] ( ) dy The expressions you obtain for the ( ) should not contain integral signs. The brackets are the bounds of integration, and the open parenthesis are the blanks. The Attempt at a...
  36. M

    Integration with Partial Fraction Decomposition

    Homework Statement \int \frac{-2x + 4}{(x-1)^{(2)}(x^{(2)}+1)}Homework Equations The Attempt at a Solution I've done the problem a couple times but the answers keep coming out differently so I'm assuming I am messing up the setup. This is what I have for the first part of the setup: -2x +...
  37. M

    Multivariable Calculus Double Integration Problem

    1. Find the volume of the region above the triangle in the xy-plane with vertices (0,0) (1,0) (0,1) and below the surface z =f(x,y)=6xy(1-x-y) My attempt is attached
  38. M

    Double Integral: Evaluate ∫∫(x^2 + y^2)dx dy in R

    Evaluate ∫∫(x^2 + y^2)dx dy over the region enclosed within R (0,0), (2,0) and (1,1). I am not asking someone to do the problem but to just verify, have I got the limits right? I split it up into 2 legs for the first leg integrate from , x: 0→1 and y :0→x for the...
  39. R

    How Do You Approach Complex Double Integrals in Polar Coordinates?

    Homework Statement Hi Guys, I need help to solve this double integration. This integration is over r and theta. The rest are constant. Homework Equations ∫^{R_{2}}_{r=0} ∫^{\pi}_{\theta=0} r^{2} sin(\theta) dr d\theta / ((D^{2}+r^{2} - 2rd cos(\theta))^{2} - R_{1}^2)^{3}, r from 0 to R_{2}...
  40. L

    Acceleration to Velocity by area integration

    I know this has been asked many times. I am integrating acceleration data from MEMS accelerometer to get velocity. I found an app note by freescale - http://cache.freescale.com/files/sensors/doc/app_note/AN3397.pdf It ignores the sampling time to calculate the area. The formula should...
  41. P

    Integration using substitution

    1. $$\int \frac{1}{1+e^x}\,dx$$ Homework Equations Substitution The Attempt at a Solution $$u=1+e^x$$ $$du=e^xdx$$ $$\int \frac{1}{u}\frac{1}{e^x}\,du$$ $$\int \frac{1}{u}\frac{1}{u-1}\,du$$ $$\int \frac{1}{u(u-1)}\,du$$ $$= \ln {|u^2-u|} = \ln {|(1+e^x)-(1+e^x)|} = \ln...
  42. P

    Integration using various techniques

    1. $$\int e^{x+e^x}\,dx$$ Homework Equations Substitution, integration by parts The Attempt at a Solution $$u=e^x$$ $$\int e^{x+e^x}\,dx = \int e^x e^{e^x}\,dx = \int ue^u\,du$$ $$a=u$$ $$da=1du$$ $$dv=e^udu$$ $$v=e^u$$ $$=ue^u-\int e^u\,du = ue^u-e^u$$ $$=e^x e^{e^x}+e^{e^x} =...
  43. W

    Asymptotic Expansion of Integrals Using Laplace's Method

    Consider the integral \begin{equation} I_n(x)=\int^{2}_{1} (log_{e}t) e^{-x(t-1)^{n}}dt \end{equation} Use Laplace's Method to show that \begin{equation} I_n(x) \sim \frac{1}{nx^\frac{2}{n}} \int^{\infty}_{0} \tau^{\frac{2-n}{n}} e^{-\tau} d\tau \end{equation} as x\rightarrow\infty...
  44. R

    MHB Laplace's Method Integration

    Consider the integral \begin{equation} I_n(x)=\int^{2}_{1} (log_{e}t) e^{-x(t-1)^{n}}dt \end{equation} Use Laplace's Method to show that \begin{equation} I_n(x) \sim \frac{1}{nx^\frac{2}{n}} \int^{\infty}_{0} \tau^{\frac{2-n}{n}} e^{-\tau} d\tau \end{equation} as $x\rightarrow\infty$. where...
  45. W

    Integration by expansion

    Consider the integral \begin{equation} I(x)= \frac{1}{\pi} \int^{\pi}_{0} sin(xsint) dt \end{equation} show that \begin{equation} I(x)= 4+ \frac{2x}{\pi}x +O(x^{3}) \end{equation} as x\rightarrow0. => I Have used the expansion of McLaurin series of I(x) but did not work. please help...
  46. R

    MHB Is McLaurin Expansion the Key to Solving Integration by Expansion?

    Consider the integral \begin{equation} I(x)= \frac{1}{\pi} \int^{\pi}_{0} sin(xsint) dt \end{equation} show that \begin{equation} I(x)= \frac{2x}{\pi} +O(x^{3}) \end{equation} as $x\rightarrow0$. => I Have used the expansion of McLaurin series of $I(x)$ but did not work. please help me.
  47. R

    MHB Laplace's Method (Integration)

    Consider the integral \begin{equation} I(x)=\int^{2}_{0} (1+t) \exp\left(x\cos\left(\frac{\pi(t-1)}{2}\right)\right) dt \end{equation} Use Laplace's Method to show that \begin{equation} I(x) \sim \frac{4\sqrt{2}e^{x}}{\sqrt{\pi x}} \end{equation} as $x\rightarrow\infty$. => I have tried using...
  48. A

    Inverse integral of this integration

    Hi I am facing a mathematical problem in my research. I am not a maths magor and i need to do this to move on with my research. Please check the picture for the equation http://i.stack.imgur.com/jQroR.jpg Mod note: Image was too large, so deleted it, and replaced it with LaTeX. Left the...
  49. K

    How Do I Compute the Integral Using u-Substitution?

    what method should i use? i tried u = x - 4 du = dx i can't continue. enlighten me please
  50. J

    Connection between summation and integration

    If exist a connection between the infinitesimal derivative and the discrete derivative $$d = \log(\Delta + 1)$$ $$\Delta = \exp(d) - 1$$ exist too a coneection between summation ##\Sigma## and integration ##\int## ?
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