What is Substitution method: Definition and 23 Discussions
In optical fiber technology, the substitution method is a method of measuring the transmission loss of a fiber. It consists of:
using a stable optical source, at the wavelength of interest, to drive a mode scrambler, the output of which overfills (drives) a 1 to 2 meter long reference fiber having physical and optical characteristics matching those of the fiber under test,
measuring the power level at the output of the reference fiber,
repeating the procedure, substituting the fiber under test for the reference fiber, and
subtracting the power level obtained at the output of the fiber under test from the power level obtained at the output of the reference fiber, to get the transmission loss of the fiber under test.The substitution method has certain shortcomings with regard to its accuracy, but its simplicity makes it a popular field test method. It is conservative, in that if it were used to measure the individual losses of several long fibers, and the long fibers were concatenated, the total loss obtained (excluding splice losses) would be expected to be lower than the sum of the individual fiber losses.
Some modern optical power meters have the capability to set to zero the reference level measured at the output of the reference fiber, so that the transmission loss of the fiber under test may be read out directly.
I'm really stuck on this one, I was able to get the answer but not by the substitution method.
So its the weight as A and B so I get A + B = 24
A(3) = B(5) so in my head I calculate a few pairs, 3 x 5 = 15 but 3 + 5 only = 8 so the next pair would be 10 and 6 which is still to small so I move...
What I have done:
I changed all fractions to common denom and that gave me
5y-5x=1 (1) *I numbered the fractions
5y+2x=5 (2)
Then: 5y=5-2x
Substitute into equation 1
(5-2x)-5x=1
5-7x=1
x=4/7
Thing is my answer says I should be getting x=0
Any hints?
Homework Statement
Question:
To solve the integral ##\int \frac{1}{\sqrt{x^2-4}} \,dx## on an interval ##I=(2,+\infty)##, can we use the substitution ##x=\operatorname {arcsint}##?
Explain
Homework Equations
3. The Attempt at a Solution [/B]
This is my reasoning, the function ##\operatorname...
Look, I was wondering if substituting the variable more than once is valid and hence the definite integral intervals change this way.
Consider the following integral (I'm working for finding the volume of a solid of revolution):
*\pi \int_{-3}^{5}3^{2}-(\sqrt{\frac{y+3}{2}}+1)^2dy
Personally I...
Homework Statement
Evaluate the following integral using a change of variables:
\int\frac{dx}{\sqrt{1-\sin^4{x}}}
Homework Equations
If f(x)=g(u(x))u'(x)
and \int g(x)dx = G(x) +C
then \int f(x)dx = G(u(x))+C
The Attempt at a Solution
It seems helpful to first simplify a little to obtain...
Homework Statement
So it says solve this wave equation :
[y][/tt] - 4 [y][/xx] = 0
on the domain -infinity<x<infinity
with initial conditions y(x,0) = e^(-x^2), yt(x,0) = x*(e^(-x^2))
Homework Equations
I used the D Alembert's solution which is 1/2(f(x+ct)+f(x-ct)) + 1/2c ∫ g(z) dz
The...
It is common that we replace \int u(x)v'(x)dx by \int udv where both u and v are continuous functions of x. My question is, must we ensure that u can be written as a function of v before applying this? The above substitution method is involved in the proof of integration by parts but I cannot...
Hello! I need help to integrate the square root of:
p x2 + x4
by the method of substitution, p is just a constant. I've been trying for a long time but I can't get it right. I know the answer and it still doesn't help. Thanks! (sorry, I don't know the Latex stuff)
Hello all
I am working on this integral
\[\int \frac{x^{2}+1}{x^{4}+1}dx\]Now, I have tried this way:
\[u=x^{2}+1\]
after I did:
\[\int \frac{x^{2}+1}{\left ( x^{2}+1 \right )\left ( x^{2}-1 \right )}dx\]
But I got stuck, I got:
\[\frac{1}{2}\cdot \int \frac{1}{u\sqrt{u-1}}dx\]
I thought...
I put it in std form, did the homogeneous test. it passed with degree 2. I substituted y=ux and dy=udx+xdu and now I'm stuck. it needs to be simplified somehow but I don't know if ux is one var or if it's u*x. Same goes for udx and xdu. Is it really u*dx+x*du? even assuming that is correct, it...
Say we are solving an indefinite integral ∫x√(2x+1) dx.
According to the textbook, the solution goes like this.
Let u = 2x+1. Then x = (u-1)/2.
Since √(2x+1) dx = (1/2)√u du,
x√(2x+1) dx = [(u-1)/2] * (1/2)√u du.
∫x√(2x+1) dx = ∫[(u-1)/2] * (1/2)√u du. <= What justifies this??
The...
Substitution method with Integration by Parts?
Homework Statement
Evaluate the integral...
∫x^3[e^(-x^2)]dx
Homework Equations
∫udv=uv-∫vdu
The Attempt at a Solution
I first tried using integration by parts setting u and dv equal to anything and everything. This seemed to make...
use the subtitution method to solve.
x^2 + 2y = 9
x - y + 3 = 0
y=x+3 -> (3)
substitute for y with x+3, you get:
x^2+2(x+3)=9 x2+2x−3=0
factorize it to get:
(x+3)(x−1)=0 x=−3,x=1
substitute for each value of x in equation 3
x=−3y=−3+3=0
x=1y=1+3=4...
Homework Statement
y'=y+y^3
Homework Equations
The Attempt at a Solution
I set y=v, dy/dx = dv/dx. Substituted back into original equation ST dv/dx = v + v^3. Cross multiply, then divide yielded dv/(v+v^3) = dx. After that, I have no clue. The book gives the following...
Homework Statement
Hi there. I'm dealing with undefined integrals now. And I found this one that I don't know how to solve.
The problem statement says: Solve the next integrals using the substitution method.
\displaystyle\int_{}^{}\displaystyle\frac{\cos(x)}{\sin^3(x)}The Attempt at a Solution...
Hi everyone,
Can you tell me how to integrate the following equation?
\int\frac{1}{x^2 + 1} \ dx
I've tried the substitution method, u = x^2 + 1, du/dx = 2x. But the x variable is still exist.
Also, the trigonometry substitution method, but the denominator is not in \sqrt{x^2 + 1}...
Homework Statement
\left( {x + y} \right)y' = x - y
Homework Equations
Back of book:
x^2 - 2xy - y^2 = C
The Attempt at a Solution
I'm not sure how to start this problem. In the examples in the book, they make a substitution, v=something, and all that was left were v's and...
Homework Statement
dy/dx = \frac{[2cos(x)^2-sin(x)^2+y^2]}{[2cos(x)]}
Substitute y(x) = sin(x) + \frac{1}{u(x)}
Homework Equations
By doing the substitution, it will yield the differential equation for u(x)
du/dx = -u tan(x) - \frac{1}{2}sec(x)
The Attempt at a Solution
I figured out i...
Evaluate the following integral using integration by substitution: http://img254.imageshack.us/img254/750/44900023cm4.png [Broken][/URL]
Here is my attempt:
Let x = sinu, then dx/du = cosu
Substituting gives, ∫1/(1-sin2u)×cosu du
= ∫1/(1-sin2u)×cosu du
= ∫cosu/√cos2u du
=...
Hi,
I have another problem about substitution Method. I think this method is used to make the problem to solve in easy way but it is making my procedure too long for this problem. Can you solve it by substitution method.
S (x+5)½/x-4 dx
where S is the sign of integral. The answer of...