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. 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...
  2. 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...
  3. 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...
  4. 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...
  5. 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...
  6. A

    MHB How Can I Simplify Real Integration Calculations?

    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 =...
  7. 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...
  8. 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...
  9. 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...
  10. 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...
  11. 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...
  12. 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. $$\int \ \frac{xe^{2x}}{(1+2x)^2},dx$$
  13. 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?
  14. 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}...
  15. 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...
  16. 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...
  17. 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...
  18. 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.
  19. 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...
  20. 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...
  21. 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) ?
  22. 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...
  23. 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: $$\\ \oint_{\partial \Omega} \omega = 0$$?
  24. 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))
  25. 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}...
  26. J

    How Do I Integrate This Sphere-Related Equation Correctly?

    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...
  27. 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...
  28. 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...
  29. H

    Can Integration by Parts Reveal Series Properties in This Integral?

    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...
  30. 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...
  31. 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...
  32. 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
  33. 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...
  34. 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...
  35. 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...
  36. A

    How Can You Integrate x/(a^2+x^2)^(3/2) Without Explicit Substitution?

    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?
  37. 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
  38. 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...
  39. 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...
  40. 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...
  41. 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?
  42. 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 =...
  43. 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...
  44. 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...
  45. 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...
  46. 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...
  47. 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
  48. 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?
  49. 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
  50. 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...
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