jee-main 2021 Q75

jee-main · India · session3_20jul_shift1 Indefinite & Definite Integrals Piecewise/Periodic Function Integration

Let $a$ be a positive real number such that $\int _ { 0 } ^ { a } e ^ { x - [ x ] } d x = 10 e - 9$ where, $[ x ]$ is the greatest integer less than or equal to $x$. Then, $a$ is equal to:
(1) $10 - \log _ { e } ( 1 + e )$
(2) $10 + \log _ { e } 2$
(3) $10 + \log _ { e } ( 1 + e )$
(4) $10 - \log _ { e } 2$

Let $a$ be a positive real number such that $\int _ { 0 } ^ { a } e ^ { x - [ x ] } d x = 10 e - 9$ where, $[ x ]$ is the greatest integer less than or equal to $x$. Then, $a$ is equal to:\\
(1) $10 - \log _ { e } ( 1 + e )$\\
(2) $10 + \log _ { e } 2$\\
(3) $10 + \log _ { e } ( 1 + e )$\\
(4) $10 - \log _ { e } 2$

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