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.
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.
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...
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...
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) ?
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...
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:
$$\\ \oint_{\partial \Omega} \omega = 0$$?
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))
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}...
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...
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...
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...
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...
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...
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...
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
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...
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...
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...
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?
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
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...
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...
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...
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?
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...
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...
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...
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...
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
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?
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
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...
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...
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...
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 +...
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
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...
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}...
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...
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...
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...
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...
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.
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...
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...