Let a be a positive real number such that $\int_{\rm{0}}^{\rm{a}} {{{\rm{e}}^{x - \left[ x \right]}}dx} {\rm{ = 10e - 9}}\,$, where [x] is the greatest integer less than or equal to x. Then, a is equal to

${\rm{10 - lo}}{{\rm{g}}_e}\left( {1 + e} \right)$

${\rm{10 + lo}}{{\rm{g}}_e}\left( {1 + e} \right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

Let a be a positive real number such that

\int_\mathrm{0}^\mathrm{a} {{\mathrm{e}^{x - \left[ x \right]}}dx} \mathrm{ = 10e - 9}\,

, where [x] is the greatest integer less than or equal to x. Then, a is equal to

View answer and explanation

Correct option: B

\mathrm{10 + lo}{\mathrm{g}_e}2

Option B is correct because the integral can be solved by splitting it into intervals of length 1, utilizing the property of the greatest integer function, and then solving for 'a'.

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

More Questions from DEFINITE INTEGRATION