JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

f: \mathbb{R} \rightarrow \mathbb{R}

is a function such that

f(x)+2 f\left(\frac{1}{x}\right)=3 x \,\forall x \neq 0

then

\int x f(x) dx

is equal to

View answer and explanation

Correct option: A

2x - \frac{1}{3}{x^3} + c

Option A (

2x - \frac{1}{3}{x^3} + c

) is correct because solving the functional equation for

f(x)

and then integrating

xf(x)

yields this result.

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