Given-2f-x-f-1-x-6x-3-x-then-1-2-f-x-dx-

Question Number 136259 by liberty last updated on 20/Mar/21

G i v e n 2 f (x) + f (\frac{1}{x}) = 6 x + \frac{3}{x}

t h e n \int_{1}^{2} f (x) d x = ?

Answered by EDWIN88 last updated on 20/Mar/21

Replacing x by \frac{1}{x} gives

\Rightarrow 2 f (\frac{1}{x}) + f (x) = \frac{6}{x} + 3 x \dots (2)

after solving we get f (x) = 3 x

\int_{1}^{2} f (x) dx = {[\frac{{3 x}^{2}}{2}]}_{1}^{2} = \frac{9}{2}

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