JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

Let

f

be a positive differentiable function defined on

(0, \infty)

and

\phi(x)=\lim \limits_{{n \rightarrow \infty}}\left(\frac{f\left(x+\frac{1}{n}\right)}{f(x)}\right)^n

Then

\int \log _e(\phi(x)) d x

is equal to

View answer and explanation

Correct option: C

\log _e(f(x))+c

Option C (

\log _e(f(x))+c

) is correct because by simplifying the limit and integrating, we can find the expression for the integral.

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