jee-main 2022 Q73

jee-main · India · session2_29jul_shift1 Integration by Substitution Substitution to Evaluate a Definite Integral (Numerical Answer)

The integral $\int _ { 0 } ^ { \frac { \pi } { 2 } } \frac { 1 } { 3 + 2 \sin x + \cos x } d x$ is equal to:
(1) $\tan ^ { - 1 } ( 2 )$
(2) $\tan ^ { - 1 } ( 2 ) - \frac { \pi } { 4 }$
(3) $\frac { 1 } { 2 } \tan ^ { - 1 } ( 2 ) - \frac { \pi } { 8 }$
(4) $\frac { 1 } { 2 }$

The integral $\int _ { 0 } ^ { \frac { \pi } { 2 } } \frac { 1 } { 3 + 2 \sin x + \cos x } d x$ is equal to:\\
(1) $\tan ^ { - 1 } ( 2 )$\\
(2) $\tan ^ { - 1 } ( 2 ) - \frac { \pi } { 4 }$\\
(3) $\frac { 1 } { 2 } \tan ^ { - 1 } ( 2 ) - \frac { \pi } { 8 }$\\
(4) $\frac { 1 } { 2 }$

Paper Questions

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