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Using method of partial fraction find the integration of f(x) when f(x) = 1/x2 – a2 and the answer is
- a)log x – a/ x + a + k
- b)log (x – a) – log (x + a)
- c)1/2a log x – a/x+a + k
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Using method of partial fraction find the integration of f(x) when f(x...
Method of Partial Fractions:
The method of partial fractions is a technique used to simplify integrands containing rational functions. It involves breaking down a rational function into simpler parts in order to integrate it more easily.
Steps to Find Integration using Partial Fractions:
1) Factorize the denominator into linear and quadratic factors.
2) Write the partial fraction decomposition.
3) Equate numerators to find the values of the constants.
4) Integrate each term of the partial fraction decomposition.
Integration of f(x) = 1/(x^2 + a^2):
1) Factorize the denominator as (x^2 + a^2) = (x + ai)(x - ai)
2) Write the partial fraction decomposition as A/(x + ai) + B/(x - ai)
3) Equating numerators, we get A(x - ai) + B(x + ai) = 1
4) Solving for A and B, we get A = B = 1/(2ai)
5) Integrating each term of the partial fraction decomposition, we get:
Integration of f(x) = 1/(x^2 + a^2) = (1/2a) ln |(x + ai)/(x - ai)|
Therefore, the correct answer is option C: 1/2a log x a / (x a + k)
The method of partial fractions is a technique used to simplify integrands containing rational functions. It involves breaking down a rational function into simpler parts in order to integrate it more easily.
Steps to Find Integration using Partial Fractions:
1) Factorize the denominator into linear and quadratic factors.
2) Write the partial fraction decomposition.
3) Equate numerators to find the values of the constants.
4) Integrate each term of the partial fraction decomposition.
Integration of f(x) = 1/(x^2 + a^2):
1) Factorize the denominator as (x^2 + a^2) = (x + ai)(x - ai)
2) Write the partial fraction decomposition as A/(x + ai) + B/(x - ai)
3) Equating numerators, we get A(x - ai) + B(x + ai) = 1
4) Solving for A and B, we get A = B = 1/(2ai)
5) Integrating each term of the partial fraction decomposition, we get:
Integration of f(x) = 1/(x^2 + a^2) = (1/2a) ln |(x + ai)/(x - ai)|
Therefore, the correct answer is option C: 1/2a log x a / (x a + k)
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Using method of partial fraction find the integration of f(x) when f(x) = 1/x2 – a2 and the answer isa)log x – a/ x + a + kb)log (x – a) – log (x + a)c)1/2a log x – a/x+a + kd)none of theseCorrect answer is option 'C'. Can you explain this answer?
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