- #1
kanika2217
- 3
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how to evaluate : ∫[(2-x)/(1-x^2)]dx...
pls ans me asap...its urgnt
pls ans me asap...its urgnt
How to evaluate : ∫[(2-x)/(1-x^2)]dx.
- Thread starter kanika2217
- Start date
In summary, the conversation is about how to evaluate the integral ∫[(2-x)/(1-x^2)]dx and the use of partial fractions to simplify the expression. The person asking for help is being reminded to be polite and to show their own work before demanding answers. The use of partial fractions is suggested as a way to approach the problem. The conversation ends with a playful reference to Britney Spears.
- #2
grzz
- 1,006
- 15
First step separate into two integrals.
- #3
arildno
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Your attitude is completely out of bounds.
These forums are upheld by private individuals who use of their spare time to offer advice.
And how do you barge in here?
by DEMANDING answers "as soon as possible", because that is somehow "urgent" for yourself.
obviously, it has been SO urgent that you haven't done anything on your own, but demand to be handed over the answers.
Do you even understand how WAY out of line you behave?
These forums are upheld by private individuals who use of their spare time to offer advice.
And how do you barge in here?
by DEMANDING answers "as soon as possible", because that is somehow "urgent" for yourself.
obviously, it has been SO urgent that you haven't done anything on your own, but demand to be handed over the answers.
Do you even understand how WAY out of line you behave?
- #4
grzz
- 1,006
- 15
arildno is quite right.
- #5
HallsofIvy
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I agree with arildno. Be polite and show us what you have done yourself.
Now, to help you do it yourself, use "partial fractions". The denominator of your fraction, [itex]1- x^2[/itex] factors as (x- 1)(x+ 1). That means we can write
[tex]\frac{2- x}{1- x^2}= \frac{A}{x- 1}+ \frac{B}{x+ 1}[/tex]
for some numbers A and B. Can you find them?
Do you know how to integrate [itex]A/(x- 1)[/itex] and [itex]B/(x+ 1)[/itex]?
Now, to help you do it yourself, use "partial fractions". The denominator of your fraction, [itex]1- x^2[/itex] factors as (x- 1)(x+ 1). That means we can write
[tex]\frac{2- x}{1- x^2}= \frac{A}{x- 1}+ \frac{B}{x+ 1}[/tex]
for some numbers A and B. Can you find them?
Do you know how to integrate [itex]A/(x- 1)[/itex] and [itex]B/(x+ 1)[/itex]?
- #6
arildno
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Britney Spears said "Whoops, I did it again!"
You ought to do as she did, HallsofIvy, with respect to the factorization..
You ought to do as she did, HallsofIvy, with respect to the factorization..
1. What is the process for solving ∫[(2-x)/(1-x^2)]dx?
To solve this integral, we first need to use partial fractions to split the integrand into simpler terms. Then, we can use techniques such as substitution or integration by parts to evaluate each term. Finally, we can combine these results to find the overall integral.
2. What are the steps for using partial fractions to evaluate this integral?
To use partial fractions, we first need to factor the denominator to find its roots. Then, we can use the coefficients of these roots to write the integrand as a sum of simpler fractions. Finally, we can use algebraic manipulation to solve for the unknown coefficients.
3. Is there a specific substitution that should be used for this integral?
Yes, the substitution u = 1-x^2 can be used to simplify the integrand and make it easier to evaluate. This will lead to a trigonometric integral that can be solved using basic integration rules.
4. Can integration by parts be used to solve this integral?
Yes, integration by parts can be used for certain versions of this integral. However, it may not be the most efficient method and could lead to a more complicated integral.
5. Are there any special cases or exceptions to keep in mind when evaluating this integral?
Yes, if the integral is evaluated over a specific interval, it is important to check for any potential singularities or discontinuities within that interval. These could affect the overall value of the integral.
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