jee-main 2014 Q84

jee-main · India · 19apr Integration by Substitution Substitution to Compute an Indefinite Integral with Initial Condition

Let, the function $F$ be defined as $F ( x ) = \int _ { 1 } ^ { x } \frac { e ^ { t } } { t } d t , x > 0$, then the value of the integral $\int _ { 1 } ^ { x } \frac { e ^ { t } } { t + a } d t$, where $a > 0$, is
(1) $e ^ { a } [ F ( x ) - F ( 1 + a ) ]$
(2) $e ^ { - a } [ F ( x + a ) - F ( a ) ]$
(3) $e ^ { a } [ F ( x + a ) - F ( 1 + a ) ]$
(4) $e ^ { - a } [ F ( x + a ) - F ( 1 + a ) ]$

Let, the function $F$ be defined as $F ( x ) = \int _ { 1 } ^ { x } \frac { e ^ { t } } { t } d t , x > 0$, then the value of the integral $\int _ { 1 } ^ { x } \frac { e ^ { t } } { t + a } d t$, where $a > 0$, is\\
(1) $e ^ { a } [ F ( x ) - F ( 1 + a ) ]$\\
(2) $e ^ { - a } [ F ( x + a ) - F ( a ) ]$\\
(3) $e ^ { a } [ F ( x + a ) - F ( 1 + a ) ]$\\
(4) $e ^ { - a } [ F ( x + a ) - F ( 1 + a ) ]$

Paper Questions

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