Let $F\left( x \right) = f\left( x \right)\,\, + \,\,f\left( {\frac{1}{x}} \right)$, where $f\left( x \right) = \mathop \smallint \nolimits_1^x \,\,\frac{{\log \,\,t}}{{1\,\, + \,\,t}}\,\,dt.\,\,{\rm{Then}},\;\,\,F\left( e \right)\,\,{\rm{equals}}$

$\begin{array}{*{20}{l}} {1/2} \end{array}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

Let

F\left( x \right) = f\left( x \right)\,\, + \,\,f\left( {\frac{1}{x}} \right)

, where

f\left( x \right) = \int \nolimits_1^x \,\,\frac{{\log \,\,t}}{{1\,\, + \,\,t}}\,\,dt.\,\,\mathrm{Then},\;\,\,F\left( e \right)\,\,\mathrm{equals}

View answer and explanation

Correct option: A

\begin{array}{llllllllllllllllllll} {1/2} \end{array}

Option A (1/2) is correct because the integral F(e) simplifies to 1/2 after applying the given function definition and substitution.