jee-main 2020 Q66

jee-main · India · session2_05sep_shift1 Integration by Substitution Substitution to Compute an Indefinite Integral with Initial Condition

If $\int \left( e ^ { 2 x } + 2 e ^ { x } - e ^ { - x } - 1 \right) e ^ { \left( e ^ { x } + e ^ { - x } \right) } d x = g ( x ) e ^ { \left( e ^ { x } + e ^ { - x } \right) } + c$, where $c$ is a constant of integration, then $g ( 0 )$ is
(1) $e$
(2) $e ^ { 2 }$
(3) 1
(4) 2

If $\int \left( e ^ { 2 x } + 2 e ^ { x } - e ^ { - x } - 1 \right) e ^ { \left( e ^ { x } + e ^ { - x } \right) } d x = g ( x ) e ^ { \left( e ^ { x } + e ^ { - x } \right) } + c$, where $c$ is a constant of integration, then $g ( 0 )$ is\\
(1) $e$\\
(2) $e ^ { 2 }$\\
(3) 1\\
(4) 2

Paper Questions

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