jee-main 2020 Q68

jee-main · India · session1_09jan_shift1 Indefinite & Definite Integrals Antiderivative Verification and Construction

If $f ^ { \prime } ( x ) = \tan ^ { - 1 } ( \sec x + \tan x ) , - \frac { \pi } { 2 } < x < \frac { \pi } { 2 }$ and $f ( 0 ) = 0$, then $f ( 1 )$ is equal to:
(1) $\frac { \pi + 1 } { 4 }$
(2) $\frac { 1 } { 4 }$
(3) $\frac { \pi - 1 } { 4 }$
(4) $\frac { \pi + 2 } { 4 }$

If $f ^ { \prime } ( x ) = \tan ^ { - 1 } ( \sec x + \tan x ) , - \frac { \pi } { 2 } < x < \frac { \pi } { 2 }$ and $f ( 0 ) = 0$, then $f ( 1 )$ is equal to:\\
(1) $\frac { \pi + 1 } { 4 }$\\
(2) $\frac { 1 } { 4 }$\\
(3) $\frac { \pi - 1 } { 4 }$\\
(4) $\frac { \pi + 2 } { 4 }$

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