jee-main 2021 Q74

jee-main · India · session1_26feb_shift2 Differential equations Integral Equations Reducible to DEs
Let $f ( x ) = \int _ { 0 } ^ { x } e ^ { t } f ( t ) d t + e ^ { x }$ be a differentiable function for all $x \in R$. Then $f ( x )$ equals:
(1) $e ^ { \left( e ^ { x } - 1 \right) }$
(2) $e ^ { e ^ { x } } - 1$
(3) $2 e ^ { e ^ { x } } - 1$
Let $f ( x ) = \int _ { 0 } ^ { x } e ^ { t } f ( t ) d t + e ^ { x }$ be a differentiable function for all $x \in R$. Then $f ( x )$ equals:\\
(1) $e ^ { \left( e ^ { x } - 1 \right) }$\\
(2) $e ^ { e ^ { x } } - 1$\\
(3) $2 e ^ { e ^ { x } } - 1$