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. Lazy Rat

    Integration problem using u substitution

    Homework Statement ## \int {sin} \frac{\pi x} {L} dx ##Homework Equations u substitution The Attempt at a Solution If i make ## u = \frac{\pi x} {L} ## and then derive u I get ## \frac {\pi}{L} ## yet the final solution has ## \frac {L}{\pi} ## The final solution is ## \frac {L}{\pi} - cos...
  2. T

    MHB How can substitution make solving integrals easier?

    Hi, I've got this problem that I've been trying to work out. I think most of my problems come from the fact that I am not yet well versed in u substitution when it comes to integrals. I'm also not 100% sure what the problem is asking. I've tried doing a couple of things, but they don't seem to...
  3. P

    MHB Raj's integration questions via Facebook

    1. The graphs intersect where the functions are equal, so $\displaystyle \begin{align*} 6 - x^2 &= 3 - 2\,x \\ 0 &= x^2 - 2\,x - 3 \\ 0 &= \left( x - 3 \right) \left( x + 1 \right) \\ x &= 3 \textrm{ or } x = -1 \end{align*}$ The higher function is $\displaystyle \begin{align*} y = 6 - x^2...
  4. D

    MHB (Integration) Find volume using disk method when rotated about the X-axis

    x = 2y - y2 x = y
  5. karush

    MHB 232.15.3.50 Reverse the order of integration in the following integral

    $\textsf{Reverse the order of integration in the following integral }$ \begin{align*}\displaystyle I&=\int_0^1 \int_2^{2e^x}f(x,y) \quad dy \, dx \end{align*} $\textit{From the integral we have that}$ $$0\leq x\leq 1 \quad \textit{and} \quad 2\leq y\leq 2e^x$$ $\textit{So, we get that}$...
  6. Wrichik Basu

    A query in integration using method of substitution

    Homework Statement :[/B] I was learning the use of standard forms in method of substitution in solving integration. My book has given this method for solving integrals of the type ##\int \frac{lx +m}{ax^2+bx+c} dx##: As an example, the book gives this one: Homework Equations :[/B] The...
  7. R

    Can someone please tell me how my book did this integration

    Homework Statement Attached is a picture.. the book went from (-1 + \frac {2}{1+u} ) du + \frac {dx}{x} = 0 Edited by moderator. to -u + 2ln(1+u) + ln(x) = ln(c) Homework EquationsThe Attempt at a Solution How in the world could the integral of 0 be ln(c)? Maybe because it's 5 am and...
  8. Ren Figueroa

    B Integration Bounds for E-field Calcualtion

    Hi guys. I’m looking at the brute force way at getting the E-field for a uniformly spherical charge distribution. The location of the E-field of interest is anywhere outside of the sphere. Here are some images Everything makes sense. I’m just not sure why the bounds for ‘s’ where z-r to...
  9. R

    Integration problem of a quotient

    Homework Statement What is the integral of e(x)2 over (x-1)2Homework Equations integral of (x-1)-2 is -(x-1)-1 and derivative of e(x)2 is 2xe(x)2 The Attempt at a Solution I tried to integrate it by part but I couldn't get a solution. I want to know how to start solving this question.
  10. M

    MHB What is the difference between ln 4 and log 4?

    I am reviewing Calculus 1 integration learned long ago in the 1990s. Integrate (1/x) dx from 1 to 4. The textbook answer is ln 4. However, many of my friends tell me that the answer can also be written as log 4. But, ln 4 does NOT equal log 4. In fact, ln 4 > log 4. Who is right? Why?
  11. ertagon2

    MHB Integration by parts, Partial fraction expansion, Improper Integrals

    - check if right check if right Now, 2 seems to be the right answer for A yet when i made x=5 and subtracted new form form the old one I got a difference of ~$\frac{4}{9}$ (should be 0 obviously) I got A=2 B=$\frac{45}{21}$ C=2 How to calculate $\lim_{{x}\to{\infty}}(- e^{-x})$
  12. D

    Deflection of Tapered Beam with Elliptic Cross Section

    I am working on deriving expression for deflection of a tapered beam with an elliptic cross-section. Hence, area moment of inertia is a linear function of the beam length. The beam is fixed at one end, and a concentrated force F is applied on its tip at the free end. I am using the known...
  13. orangeraindrops

    What does the area under a volume vs time graph represent?

    Homework Statement I have a function showing the volume of water in a bay at different times in the day, and I want to know what the area under this curve would represent (if it represents anything meaningful). I know how to integrate, so that isn't a problem. Homework Equations I am...
  14. D

    Integration for the Volume of an Ellipsoid

    Homework Statement Let E be the ellipsoid x^2 + 2xy +5y^ +4z^2 = 1 Find the Volume of E Homework Equations None, just various integration methods. The Attempt at a Solution I know we're not supposed to say 'I don't know where to start' but with this one I really don't. If the best approach...
  15. J

    MHB Differentiation / Integration Help

    The curve has a gradient function dy/dx = 2 +q/(5x^2) where q is a constant, and a turning point at (0.5, -4). Find the value of q. option 1 : 2.5 option 2: -2.5 option 3: 0 Option 4: -3 I couldn't find the answer and will need assistance to how the answer can be obtained. I have...
  16. M

    Change integration limits for cylindrical to cartesian coord

    Homework Statement I want to change the integration limits of an integral in cylindrical to cartesian coordinates. For example the integral of function f(r) evaluated between b and R: ∫ f(r)dr for r=b and r=R (there is no angular dependence). For write de function in cartesian coordinates...
  17. C

    Python Numerical integration 'quad' error

    I have defined a series of functions below with the end function `fA` being inserted for a numerical integration. The integration is with respect with one variable so the other arguments are passed as numeric so that the integration method (quad) may proceed import numpy import...
  18. alijan kk

    Leibniz Integral Rule Explained

    1. The problem statement, a ll variables and given/known data Homework Equations The Attempt at a Solution what is t equal to here , how should i think it ?
  19. W

    Vector Integration: Fundamental theorem use

    Homework Statement Could someone illustrate why $$\int_{V} \nabla \cdot (f\vec{A}) \ dv = \int_{V} f( \nabla \cdot \vec{A} ) \ dv + \int_{V} \vec{A} \cdot (\nabla f ) \ dv = \oint f\vec{A} \cdot \ d\vec{a}$$ ? Homework EquationsThe Attempt at a Solution I understand that the integrand can...
  20. F

    Calculate Electric Flux from Point Charge to Plate:

    Homework Statement A ##10 cm## (on y axis) by ##10 cm## (on z axis) flat plate is located ##5 cm## away (on x axis) from a point charge ##q##. Calculate the electric flux from the point charge to the plate. Can somebody solve it using surface integral using both spherical and cartesian...
  21. chwala

    Find f'(x): f'(x) = ##\frac {dy} {dx},\frac {dx}{dt}= \frac {8t^7}{1+t^{16}} ##

    Homework Statement if ## f(x)= \int_x^3 \sqrt {1+t^{16}} dt ## find f'(x)Homework EquationsThe Attempt at a Solution let ## x = 1+t^{16},## → ##\frac {dx}{dt},= 16t^{15},## ## y= x^{1/2} ## →##\frac {dy} {dx},= 0.5x^{-0.5}##
  22. M

    MATLAB Numerical Integration with variable limits MATLAB

    Hi PF! Suppose I have two functions ##f(x),\,g(y)## that are numerically defined as vectors (i.e. ##g(y) = [0,1,4,9,16]:y = [0,1,2,3,4]## and say ##f(x) = [0,1,8,27,64]:x = [0,1,2,3,4]##) and am trying to compute $$\int_0^1 f(x) \int_x^1 g(y)\, dydx.$$ How would I do this in MATLAB? I could be...
  23. Peter Alexander

    Understanding the Cauchy Integration Formula for Analytic Functions

    Hello everyone! I'm having a bit of a problem with comprehension of the Cauchy integration formula. I might be missing some key know-how, so I'm asking for any sort of help and/or guideline on how to tackle similar problems. I thank anyone willing to take a look at my post! Homework Statement...
  24. J

    Double Integration Homework: Changing Limits

    Homework Statement Homework Equations I've drawn graph below. The Attempt at a Solution Currently their limits are y = 0 to y = x - 2 vertical arrow and x = 2 to x = infinite. horizontal arrow Changing limits i get right side graph. x = y + 2 to x = infinite horizontal arrow y = 0 to y =...
  25. C

    Solving Contour Integration Homework

    Homework Statement For R > 0, assume ΓR is a circle {z ∈ C : |z| = R} with anticlockwise direction. For which R>0, does the the function f(z) = 1/sin^(2)(z) be continuous on ΓR and evaluate ∫_{ΓR} dz/sin^(2)(z) for each R (the answer may be dependent on R). Homework Equations sinx= (e^(ix)...
  26. V

    Integration with Respect to x: Integral of sqrt((5-x)/x)

    Homework Statement integration with respect to x Homework Equations integral 1/sqrt (a^2 - x^2) = arcsin(x/a) The Attempt at a Solution image attached, the arcsine term in 5/2 arcsin((2x-5)/5) it should be 5 arcsine(sqrt(x/5))
  27. R

    Easy matrix integration question

    Homework Statement This is just the triple integral of an easy matrix problem. I just have no ideas what they got by the time they got to the integral of x. Homework Equations integral[/B]The Attempt at a Solution Somebody please prove me wrong. I got a matrix of constants by the time I got...
  28. T

    I Integration above or below axis

    If you are trying to find the integral of a function with a complex pole on the real axis (i.e. ##[-\infty,\infty]##) via analytic continuation, does it matter if you integrate along a contour either in the upper-half plane or lower-half plane? I was under the assumption that either approach was...
  29. R

    I Solving Integration by Parts for Relativistic Kinetic Energy

    Hi, I've been following a derivation of relativistic kinetic energy. I've seen other ways to get the end result but I'm interested in finding out where I've gone wrong here: I'm struggling with integrating by parts. The author goes from...
  30. S

    Solve Tricky Integration: ##\frac{20\ln{(t)}}{t}##

    Homework Statement How do I solve ##\frac{20\ln{(t)}}{t}##? Homework EquationsThe Attempt at a Solution Is it easier to calculate this without integrating by parts? I'm not sure where to start.
  31. C

    How to Convert Rectangular Integrals to Polar Coordinates Correctly?

    Homework Statement Trying to help a friend with a problem. We are supposed to solve the below using polar coordinates. The actual answer is supposed to be π/16. Solving the integral is not the issue, just converting it. 2. The attempt at a solution What I got sort of worked, but it is only...
  32. EastWindBreaks

    I dont understand this integration

    Homework Statement in the textbook, it says: how does the integral of y'' gives you y' like that? Homework Equations given C_a is a dimensionless peak acceleration factor. The Attempt at a Solution [/B]
  33. I

    I Dirac-Delta Function, Different Integration Variable

    Hello, I know that the derivative of Dirac-delta function (##\delta'(x-x') = \frac{d}{dx} (\delta(x-x')))## does the following: ##\int_{-\infty}^{\infty}\psi(x')*\delta'(x-x') dx' = \frac{d\psi(x)}{dx}## it is easy to visualize how the delta function and the function ##\psi(x')## interact along...
  34. M

    Integration of an interaction force to find potential energy

    Homework Statement A particle that can move along the x-axis experiences an interaction force Fx=(3x2−5x) N where x is in m. Find an expression for the system's potential energy. Express your answer in terms of the variables x and the constant of integration C, where C is in joules. Homework...
  35. Lazy Rat

    Integration of an equation relating to electrostatics

    Homework Statement Hi I was wondering if anyone could give me a hand with this problem I'm trying to solve. I am trying to integrate this equation twice. I'm not really sure what to do with the right hand side of the equation.Homework Equations The Attempt at a Solution [/B] The left side...
  36. yeshuamo

    Variable of integration in geometric phase calculation

    Homework Statement Calculate the geometric phase change when the infinite square well expands adiabatically from width w1 to w2.Homework Equations Geometric phase: \gamma_n(t) = i \int_{R_i}^{R_f} \Bigg< \psi_n \Bigg | \frac{\partial \psi_n}{\partial R} \Bigg > dR Infinite square well wave...
  37. Z

    Simple integration to find area

    Homework Statement I wish to find the area under the curve y = 1/2^x between x=0 and x=1 but get an answer that is half the expected answer.Homework Equations Integrate y = 1/2^x to get -1/(2^x ln2) + Const This integration result was confirmed on Wolfram Slot in the range x = 0 to x = 1...
  38. P

    I Numerical Integration twice (acceleration to displacement)

    Hello everyone I have the following question regarding numerical integration twice from acceleration to displacement. Suppose that a particle has acceleration function of a = tt (which has non-elementary integral), to find the velocity it is easy as I can use Simpson's rule for numerical...
  39. V

    Can you handle this integration with limits problem?

    Homework Statement Integrate ∫ (tan √x) / (2 √x) dx Homework Equations Limits from 0 to ∞ The Attempt at a Solution Put u = √x du/dx = 1/ (2 √x) dx = du * (2 √x) now question becomes ∫ tan u du = log sec u = log (sec √x) now applying limits ∫ tan u du = log (sec √∞) - log (sec √0) = log...
  40. Q

    Help with bounds for integration

    Homework Statement I'm trying to change the bounds for this integral Sin(x^2)dxdy With x going from 1 to 2y, y going from 0 to 1 (I already know the integration for sin(x^2) The Attempt at a Solution I converted 2y=x to 1/2x=y and graphed all the bounds. I went with 1,2 for my...
  41. yecko

    Triple integration - find volume

    Homework Statement Homework Equations in the pic The Attempt at a Solution why is there an extra "r" in the highlighted line? my attempt: ## \int_0^{2\pi}\int_0^2\int_{r^2}^41\ dy\ r\ dr\ d\theta ## = ##\int_0^{2\pi}\int_0^2\left(4-r^2\right)\ r\ dr\ d\theta## thanks
  42. L

    Finding the Expression for v Using Partial Integration

    Homework Statement For an analytic function, f(x+iy)=u(x,y)+iv(x,y),u is given by u=(3x^2) -(3y^2). The expression for v, considering K to be a constant is? Homework Equations δu/δx=δv/δy δu/δy=-δv/δx [/B] The Attempt at a Solution My attempt :- u=(3x^2) -(3y^2) δu/δx=6x &...
  43. S

    Can Wolfram Mathematica be wrong on this Integration?

    Homework Statement Mathematica vs (Symbolab + my brain) Homework EquationsThe Attempt at a Solution I think this integral calculation in Mathematica is wrong. Open pictures below. Please help me. Graphs (the red one is under the blue and the green): https://ibb.co/bACa3G Wolfram Mathematica...
  44. Alexanddros81

    Simple Pendulum motion - Numerical Integration

    Homework Statement The differential equation of motion for the simple pendulum can be shown to be ##\ddot {θ} = -(g/L)sinθ##. Given that L=9.81 m and that the pendulum is released from rest at θ=60deg, determine the time required for the pendulum to reach the position θ=0deg. Use Δt=0.10s, and...
  45. L

    Integration of even powers of sine and cosine

    Homework Statement Homework Equations cos2x = (1+cos2x)/2 sin2x = (1-cos2x)/2 The Attempt at a Solution I believe you would use the double angle formula repeatedly but that is very tedious; is there a more concise way to solve the problem?
  46. F

    Converting Simulink model to C code, integration

    Dear Forumers,Given a simulink model: http://www.femm.info/Archives/contrib/images/TransientLoudspeaker/SimulinkOverview.png I would like to implement fast code for it.I have no access to matlib or simulink at all, so I tried to implement the simulation in C code. Code for the block...
  47. S

    I How Does Nakahara Compactify I=[0,1] to S^1 in De Rham Cohomology Proof?

    Hello! In Nakahara's Geometry, Topology and Physics in chapter 6.4.5 second edition, he proves at a point that on a simply connected manifold, the first de Rham cohomology group is trivial. In the proof he defines ##\alpha : I=[0,1] \to M##, homotopic to a point. Now, by the rules of integration...
  48. N

    Integration by parts/substitution

    Hi. I think I jumped too eagerly into my latest module, as I am positive it makes many assumptions on previous experience. I am obviously lacking. I have created a question in Word, but the equations don;t appear to be copying into this thread. So I have uploaded question instead. If this is...
  49. Q

    Triple Integration: Solve Homework Equation

    Homework Statement I'm trying to figure out the other parameters to solve the problem Homework Equations I know sqrt(x^2+y^2+z^2) = p The Attempt at a Solution I changed the integrand to p^3 sin(theta) since p * p^2 sin(theta) Then for the first integration sign, I know how to get the...
  50. Math Amateur

    MHB Why Does Theorem 1.9 Use f(t) Instead of f(γ(t))?

    I am reading John B. Conway's book, "Functions of a Complex Variable I" (Second Edition) ... I am currently focussed on Chapter IV: Complex Integration ... Section 1: Riemann-Stieljes Integral ... ... I need help in fully understanding the first example on page 63 ... ... The the first...
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