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. G

    B From dE=dm*c^2 to E=m*c^2: Integration constant?

    Hi, I've read some high school "derivations" of ##E=m\cdot c^2## that all considered single photons with momentum ##p=E/c## that are absorbed or emitted from some massive object, changing its mass. So they actually only showed the incremental $$\Delta E=\Delta m\cdot c^2 .$$ Most of those...
  2. RubiksMelia

    Constant of Integration when calculating displacement

    Homework Statement The speed of a pendulum bob moving in simple harmonic motion is given by v = 1.26sin(2πt) where v is in m/s and t is time in seconds. Homework Equations s = ∫ v dt The Attempt at a Solution v = 1.26sin(2πt) Integrating v yields s = -0.2cos(2πt) + c and solving for c...
  3. C

    Integration by Parts: Solving Integrals with √(1+x^2) and x

    Homework Statement [/B] Homework Equations ∫ f(x) g'(x) dx = f(x) g(x) - ∫ f '(x) g(x) dx f(x)=√(1+x^2) f '(x)=x * 1/√(1+x^2) g'(x)=1 g(x)=x The Attempt at a Solution ∫ √(1+x^2) * 1 dx =x * √(1+x^2) - ∫ x^2 * 1/√(1+x^2) dx Further integration just makes the result look further from what...
  4. N

    Integrating with Substitution: Solving for ∫(3x^2+x)(2x^3+x^2)^2 dx

    Homework Statement dz/dx=(3x2+x)(2x^3+x^2)^2[/B]Homework Equations ∫(3x^2+x)(2x^3+x^2)^2 dx The Attempt at a Solution I tried substituting (2x^3+x^2) Let t= 2x^3 + x^2 dt=6x^2+2x dx dt/dx= 6x^2+2x I can only solve till this point . I don't have any clue how to solve it further But how do we...
  5. GIM

    Change of the order of integration including Dirac delta

    Can somebody help me? I am studying Faddeev-Popov trick, following the Peskin and Schroeder's QFT book, but I can't understand one thing. After they inserted the Faddeev-Popov identity, $$I = \int {{\cal D}\alpha \left( x \right)\delta \left( {G\left( {{A^\alpha }} \right)} \right)\det \left(...
  6. E

    B What would the "correct" way of doing this integral be?

    v(x(t)), where v represents velocity and is a function of position which is a function of time. I have the equation: v dv/dx = 20x + 5 and want to solve for velocity. The way our professor solved it was by multiplying both sides by dx and integrating => ∫v dv = ∫20x+5 dx. I know doing this is...
  7. Jatin Kaushal

    B Why do we put the dot multiplication symbol when integrating

    This is I think a really dumb question, but I never got it, why do we have that dot symbol when we integrate. Like in gauss's law, we have ∫E⋅dA . why is that ⋅ there? Thank you for your help
  8. ShayanJ

    A Wrong integration in Sakurai-Napolitano(and Fetter-Walecka)?

    In chapter 7 of "Modern Quantum Mechanics" 2nd edition by Sakurai and Napolitano, a treatment of the degenerate electron gas is given as an example for 2nd quantization. This treatments is mostly taken from the same material in chapter 1 of "Quantum theory of many particle systems" by Fetter and...
  9. J

    I Need help with this definite integral

    I'm having a tough time with this integral: $$\int_{0}^\infty \frac{x^2 \, dx}{x^4+(a^2+\frac{1}{b^2})x^2+\frac{2a^2}{b^2}}$$ where $$a, b \in \Bbb R^+$$ I tried using the residue theorem, but the roots of the denominator I found are quite complicated, and I got stuck. What contour should I...
  10. FatalFlare

    Why Does Leg Selection in Trig Substitution Affect the Integral Result?

    I used trig substitution and got sqrt(x^2-9)+3*arcsin(3/x) which seems to be incorrect when I check it in my calculator and the textbook. I made a right triangle where one of the legs was sqrt(x^2-9) and it so happens that if you switch the leg the answer becomes sqrt(x^2-9) -...
  11. davidbenari

    I Numerical integration of PDEs: How do you satisfy boundary conditions

    Suppose we are solving a diffusion equation. ##\frac{\partial}{\partial t} T = k\frac{\partial^2}{\partial x^2} T## On the domain ##0 < x < L## Subject to the conditions ##T(x,0) = f(x) ## and ##T = 0 ## at the end points. My question is: Suppose we solve this with some integration scheme...
  12. T

    I Vector Triple Product Identity and Jacobi Identity for Deriving 4B.10 and 4B.11

    I was trying to derive the following results from 4B.8 as suggested by using the vector triple product identity but have been unsuccessful in deriving ##\vec{L_R}## and ##\vec{S_R}## in the end. After using the identity and finding the integrand to be ## \vec{E}(\vec{r}\cdot\vec{B}) - \vec{B}...
  13. F

    MATLAB Finite difference numerical integration or ode45?

    I'm trying to numerically solve the time dependent Schrödinger equation and I've been told that the best approach is to numerically integrate using a finite difference method, however I don't understand why I couldn't just use ode45 to solve it?! Is the finite difference (interpolation) method...
  14. S

    How Does Gravity Vary Inside the Earth?

    Homework Statement The question is pretty long and wordy so apologies in advance! Inside the Earth the gravitational field falls off linearly as one approaches the centre. An accurate description of motion in a very deep hole would therefore be to use Newton’s law, f = ma, but with the force...
  15. F

    Volume enclosed by two spheres using spherical coordinates

    Homework Statement Use spherical coordinates to find the volume of the solid enclosed between the spheres $$x^2+y^2+z^2=4$$ and $$x^2+y^2+z^2=4z$$ Homework Equations $$z=\rho cos\phi$$ $$\rho^2=x^2+y^2+z^2$$ $$dxdydz = \rho^2sin\phi d\rho d\phi d\theta$$ The Attempt at a Solution The first...
  16. C

    MATLAB Numerical Integration with Matlab - Solve K33, K11 Integral

    Hi all, i need help solving the following integral using Matlab: * tetam is a parameter and the integration is by alpha. the answer should be function of tetam * K33, K11 are constantsThanks , Chen
  17. S

    This allows you to compute the integral as a function of the difference ε.

    Homework Statement ∫ from 2 to 6 of dx/(x-4) Homework Equations None The Attempt at a Solution u=x-4 du=dx ln abs value x-4 abs value ln2-ln2=0 What am I doing wrong?
  18. JulienB

    Damped and undamped oscillations (integration?)

    Homework Statement Hi everybody! I'm doing a problem about oscillations, and I must admit that a few things are still unclear to me about that subject. Can someone maybe help me? a) A onedimensional masspoint m is oscillating under the influence of the force F(x) = -c⋅x (c > 0). What is the...
  19. P

    Contour integration by parametisation

    Homework Statement Determine, by explicit parameterisation, ∫C dz f(z), where f(z) = z^n , n ∈ Z, n > 0 and C is the line segment from z = 0 to z = 2 together with the line segment from z = 2 to z = 2 + i. Homework Equations ∫ϒ f(z) dz = ∫ab dt f(ϒ(t))ϒ'(t) where ϒ'(t)≈dz/dt The Attempt...
  20. S

    How Do You Reverse the Limits of Integration for a Sine Function?

    Homework Statement Switch the order of integration: ∫∫f(x,y) dydx, with 0≤x≤π/2, 0≤y≤sin(x) The Attempt at a Solution ∫∫f(x,y) dxdy, with sin(x)≤x≤π/2, 0≤y≤sin(x) The upper bound of x is π/2, while the lower bound is sin(x). It's just the first 1/4 of the area of a sine wave. The upper...
  21. S

    Integration of a Triangle: Evaluating ∫∫D sin(x) / x dA

    Homework Statement Evaluate ∫∫D sin(x) / x dA, where A is the triangle with vertices (0, 0),(0, 1),(1, 1). Homework EquationsThe Attempt at a Solution I've set up the integral, with x≤y≤x^2, 0≤x≤1 for the upper and lower bands of each integral. dxdy I'm not sure how to go about it though. I...
  22. Hepth

    Mathematica Another bug? Weird integration results.

    I can't upload the notebook I guess, that would be a nice feature mods! (.nb extension) But here is my code , there seems to be a problem with integrating separately and then combining. $Assumptions = 0 < r < 1 && 0 < z < 1; FUNCTION = Expand[-(Pi*(-1 + r)*(-12*z + r^2*z + r*(-12 +...
  23. R

    MATLAB Bisection method and numerical integration

    In Matlab I am trying to use the composite Simpson's rule to find ##x_l## so that $$170=\int^{x_l}_0 \sqrt{1+(y')^2} dx = \int^{x_l}_0 \sqrt{1+\left( \frac{x^2}{68000} \right)^2} dx $$ For convenience this can be written as $$I(x) = 170 - \int^x_0 \sqrt{1 + (\frac{x^2}{68000})} dx$$ The...
  24. E

    I Is my integral integrable using Mathematica or is there a fundamental error?

    After following the logical steps to derive something, I reached to the following integral: \int_0^{\infty}\frac{1}{x^2}\exp\left(\frac{A}{x}-x\right)E_1\left(B+\frac{A}{x}\right)\,dx where ##E_1(.)## is the exponential integral function, and ##A## and ##B## are non-zero positive constants. I...
  25. S

    I Integration of 1 variable in 2 different ways.

    I have to do a integration which goes like this: (V-M)(dP/dx)+3P(dV/dx)=0, (where M,P and V are constants). If you integrate with dx, you will get: ∫[(V-M)dP]+∫[3PdV]=0. which ultimately results in the answer M=4V. Now, i can put the first equation in this form also...
  26. Brandon Trabucco

    B Complex Integration By Partial Fractions

    Hello, I am enrolled in calculus 2. Just having started a section in our textbook about integration by partial fractions, I eagerly began trying to use this integration technique wherever I could. After messing around for multiple days, I ran into this problem: ∫ 1/(x^2+1)dx I immediately...
  27. P

    Complex Analysis: Contour Integration Question

    Homework Statement State, with justification, if the Fundamental Theorem of Contour Integration can be applied to the following integrals. Evaluate both integrals. \begin{eqnarray*} (i) \hspace{0.2cm} \int_\gamma \frac{1}{z} dz \\ (ii) \hspace{0.2cm} \int_\gamma \overline{z} dz \\...
  28. V

    Prove the integral is in the range of f

    Homework Statement If f: [0,1] \rightarrow \mathbb{R} is continuous, show that (n+1) \int_0^1 x^n f(x) \mathrm{d}x is in the range of f Homework Equations (n+1) \int_0^1 x^n f(x) \mathrm{d}x=\int_0^1 (x^{n+1})' f(x) \mathrm{d}x The Attempt at a Solution I tried integration by parts, but that...
  29. N

    Changing Order of Triple Integration

    Homework Statement \int_0^5 \int_0^2 \int_0^{4-y^2}\ \, dxdydx Change order to dydxdz Homework EquationsThe Attempt at a Solution I'm confused mainly because the limits are mostly numbers, not functions. I graphed the limits in @D and #d and this is what I got: \int_0^{4-y^2} \int_0^5...
  30. S

    A Integration of Schrodinger equation

    I'm trying to integrate the Schrodinger equation ##i\hbar \frac{d}{dt} |\psi(t)\rangle = H |\psi(t)\rangle## with the initial condition ##|\psi(t_{0})\rangle=|\psi_{0}\rangle## to show that ##|\psi(t)\rangle = \exp(\frac{t-t_{0}}{i\hbar}H)|\psi_{0}\rangle##. I know how to plug in the solution...
  31. C

    Solving Deflection Using Double Integration: Simplify or Integrate?

    When using the double integration method to solve for deflection, do you simplify the integral before integrating or do you just integrate it? When i tried it with simplifying and without simplifying, I get a different value for the constant which results in different answers. For example in...
  32. Korbid

    How to Numerically Solve a Multiple Integral in Mathematica or Sage?

    I'm trying to solve numerically this multiple integral. But i don't know how to calculate it with Mathamtica or Sage software. $$\int{e^{-(\vec{v}^2_1+\vec{v}^2_2)}e^{-E(\tau)}}d\vec{r}_1d\vec{r}_2d\vec{v}_1d\vec{v}_2$$ $$E(\tau)=\frac{k}{\tau^2}e^{-\tau/\tau_0}$$...
  33. S

    How to Integrate to find velocity as a function of time

    Homework Statement dv/dt = -βv Integrate to find velocity as a function of time, assume the particle's initial velocity is v0. β is constant v = velocity (not constant) t = time Homework EquationsThe Attempt at a Solution dv = -βvdt ∫dv = -β∫vdt --------> limits of integration for the right...
  34. D

    Differentiation and integration

    Homework Statement Hi,I saw a statement in my physics notes like this(Anyway it is a maths problem): where L is a general differential operator.G is a green's function(I guess it is irrelevant) My question is related to the red line: Suppose we have this: ∂/∂x ∫ f(x-y)g(y) ∂y is it...
  35. The-Mad-Lisper

    Need Help with Integration for Solving ODE

    Homework Statement \frac{dy}{dx}=y^2-1 y(0)=3 Homework Equations \frac{dy}{dx}=f(y) \leftrightarrow \frac{dx}{dy}=\frac{1}{f(y)} The Attempt at a Solution \frac{dx}{dy}=\frac{1}{y^2-1} dx=\frac{dy}{y^2-1} \int dx=\int \frac{dy}{y^2-1}+C x=\int \frac{dy}{y^2-1}+C How do I integrate \int...
  36. Cincin

    Difficult integral - Falling mass

    Homework Statement Solve the differential equation, dt/dv= 1/g (1/1-a^2*v^2) where a = (k/mg)^1/2 to yield v= 1/a(1-e^-2agt/1+e^-2agt). Homework Equations F=ma Newton's 2nd Law Integration Laws The Attempt at a Solution See image. I think I'm getting messed up on the integration laws.
  37. K

    Find the Mistake in Calculating Volume by Integration

    Homework Statement I have the attached problem ,and Show my answer and solution, My answer is 3.14*(15 -8ln4) While book answer 3.14(15+8ln) Can anyone point to the mistake I made?
  38. G

    Integration of irrational function

    Homework Statement Find the integral \int \frac{1}{(x-2)^3\sqrt{3x^2-8x+5}}\mathrm dx 2. The attempt at a solution I can't find a useful substitution to solve this integral. I tried x-2=\frac{1}{u},x=\frac{1}{u}+2,dx=-\frac{1}{u^2}du that gives \int \frac{1}{(x-2)^3\sqrt{3x^2-8x+5}}\mathrm...
  39. G

    Integration with power substitution

    Homework Statement Find the integral \int \frac{2\sqrt[5]{2x-3}-1}{(2x-3)\sqrt[5]{2x-3}+\sqrt[5]{2x-3}}\mathrm dx 2. The attempt at a solution...
  40. T

    Integration of Maxwell speed distribution function

    Homework Statement Show the steps needed to obtain the equation for average molecular speed, cavg=√8RT/πM from the integral (from negative infinity to infinity) ∫v*f(v)dv where f(v) is the Maxwell distribution of speeds function f(v)=4π*(M/2πRT)1.5v2e-Mv2/2RT M is the molar mass of the...
  41. Oaxaca

    I Integration leading to ERFI solutions

    I am attempting to normalize a wave function and need to integrate ##\int A^2*e^{(\lambda^2x^2)} dx## going from -inf to +inf. I tried to integrate this on Wolfram Alpha and this was the result. Upon integrating with the parameters the solution is as such. How does the erfi get removed? Do I...
  42. N

    Integrate √1+x^2 - Solutions & Explanations

    1. The problem is as follows: ∫(√1+x^2)dx/(x) 2. Using trig sub --> x = atanΘ with a = √1 = 1. So x = tanΘ and dx = sec^2ΘdΘ. 3. Picture included of attempted solution. I tried u substitution with both u = secΘ and u=tanΘ but didn't have the right du...
  43. Noriele Cruz

    I Miscellaneous Integration Technique

    We were taught of several integration technique, only to find one of those techniques came up as years of solving of our professor.. Can someone explain to me how substitution x = 1 / z dx = -dz / z^2 works for some problems? He called this reciprocal substitution, as what you can literally...
  44. matt_crouch

    Maple Can Maple Show Step-by-Step Solutions for Complex Contour Integrals?

    Is it possible to get Maple to show me step by step how to solve a complex contour integral? f := (x,y,z,v) -> (x+I*x*cos(v)+I*y*sin(v))^(-2) int(f(x,y,z,v),v=0..2*Pi) assuming(x,real,y,real,z,real,v,real) But I would like to know how Maple solves this step by step. I tried using the tutor...
  45. C

    One dimensional integration that Mathematica cannot do

    I want to evaluate $$\int_{a+b-c}^s\,\text{d}x\, \frac{(-x+ab/c)^{\epsilon}}{(x+c-a-b)^{\epsilon+1} (a-x)},$$ where ##a,b,c,\epsilon## are numbers, and to be treated as constants in the integration. I put this into mathematica and an hour later it is still attempting to evaluate it so I aborted...
  46. TheDemx27

    I Cauchy Repeated Integration Explanation?

    https://anhngq.wordpress.com/2013/04/25/the-cauchy-formula-for-repeated-integration/ Could someone please explain, bit by bit, how the formula works? For instance, why are we integrating with respect to sigma, up to sigma in the equation before it?
  47. H

    I What is "making the time integration redundant"?

    What does it mean by "making the time integration redundant" (5th line)? If I let ##t_2=t_1##, I will only get ##0=0-0##. Source: http://www.phys.ufl.edu/~maslov/classmech/flannery.pdf
  48. MrGianmarcoD

    I Hydrost Pressure Integration Problem (Environmental Physics)

    Hey guys! I'm working on a problem for which i somehow just can't figure out what I'm doing wrong. This is the problem: I think I've figured it out, but somehow i think i make an error with the maths. First of let's determine the equation for the temperature (in Kelvin): $$T(z) =...
  49. Kara386

    Tricky integration (maybe delta function)

    Homework Statement I need to integrate ##\frac{A}{2a\sqrt{2\pi}} \int_{-\infty}^{\infty} \frac{e^{ik(x+x')}}{(b^2+k^2)}dk## I have tried substitution and integration by parts and that hasn't worked. I can see that part of it is the delta function, but I don't really know how to use that fact...
  50. Ethan Godden

    Integration with trig substitution

    Homework Statement The problem is the integral attached Homework Equations sec2(u)=(1+tan2(x)) a2+b2=c2 ∫cos(u)=-sin(u)+C The Attempt at a Solution The solution is attached. I am wondering if someone could give me a hint where I went drastically wrong or where I possibly dropped a negative...
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