If $2\,f\left( x \right)\,\, - \,\,3\,f(1/x) = x,\;\,\,{\rm{then}}\,\,\mathop \smallint \nolimits_1^2 \,\,f\left( x \right)dx$ is equal to

$\left( {3\,\,/\,\,5} \right)\,\,\log \,\,2$

$\left( { - \,3\,\,/\,\,5} \right)\,\,\log \,\,2$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

2\,f\left( x \right)\,\, - \,\,3\,f(1/x) = x,\;\,\,\mathrm{then}\,\,\int \nolimits_1^2 \,\,f\left( x \right)dx

is equal to

View answer and explanation

Correct option: B

\left( { - \,3\,\,/\,\,5} \right)\,\,(1 + \log \,\,2)

Option B ((-3/5)(1 + log 2)) is correct because it is the result of solving the given functional equation and then evaluating the definite integral.

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