JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

If for non-zero

x, a f(x)+b f\left(\frac{1}{x}\right)=\frac{1}{x}-5

, where

a \neq b

, then

\int\limits_{1}^2 f(x) d x=

____.

View answer and explanation

Correct option: A

\frac{1}{a^2-b^2}\left[a \ln 2+\frac{7 b}{2}-5 a\right]

Option A (

\frac{{1}}{{a^2-b^2}}[a \ln 2+\frac{{7b}}{{2}}-5a]

) is correct because it is the result of solving the system of equations for f(x) and then integrating from 1 to 2.

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