Maths-
General
Easy
Question
The partial fractions of
are
Hint:
In order to integrate a rational function, it is reduced to a proper rational function. The method in which the integrand is expressed as the sum of simpler rational functions is known as decomposition into partial fractions. After splitting the integrand into partial fractions, it is integrated accordingly with the help of traditional integrating techniques.
The stepwise procedure for finding the partial fraction decomposition is explained here::
- Step 1: While decomposing the rational expression into the partial fraction, begin with the proper rational expression.
- Step 2: Now, factor the denominator of the rational expression into the linear factor or in the form of irreducible quadratic factors (Note: Don’t factor the denominators into the complex numbers).
- Step 3: Write down the partial fraction for each factor obtained, with the variables in the numerators, say A and B.
- Step 4: To find the variable values of A and B, multiply the whole equation by the denominator.
- Step 5: Solve for the variables by substituting zero in the factor variable.
- Step 6: Finally, substitute the values of A and B in the partial fractions.
The correct answer is: 
Given :

Step 1: While decomposing the rational expression into the partial fraction, begin with the proper rational expression.

Splitting 5x + 2 in the numerator

Thus, the partial fractions of
are 
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can never become positive.
Reason : f(x) = sgn x is always a positive function.
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=
=
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is
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If I =
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The indefinite integral of
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If f
= x + 2 then
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If f
= x + 2 then
is equal to
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Let
, then
is equal to:
Let
, then
is equal to:
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Statement I : y = f(x) =
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R Range of f(x) is [3/4, 1)
Statement II :
.
Statement I : y = f(x) =
, x
R Range of f(x) is [3/4, 1)
Statement II :
.
maths-General