jee-main 2024 Q88

jee-main · India · session2_05apr_shift2 Standard Integrals and Reverse Chain Rule Definite Integral Evaluation via Substitution or Standard Forms
If $f ( t ) = \int _ { 0 } ^ { \pi } \frac { 2 x \mathrm {~d} x } { 1 - \cos ^ { 2 } \mathrm { t } \sin ^ { 2 } x } , 0 < \mathrm { t } < \pi$, then the value of $\int _ { 0 } ^ { \frac { \pi } { 2 } } \frac { \pi ^ { 2 } \mathrm { dt } } { f ( \mathrm { t } ) }$ equals $\_\_\_\_$ 
If $f ( t ) = \int _ { 0 } ^ { \pi } \frac { 2 x \mathrm {~d} x } { 1 - \cos ^ { 2 } \mathrm { t } \sin ^ { 2 } x } , 0 < \mathrm { t } < \pi$, then the value of $\int _ { 0 } ^ { \frac { \pi } { 2 } } \frac { \pi ^ { 2 } \mathrm { dt } } { f ( \mathrm { t } ) }$ equals $\_\_\_\_$
Paper Questions
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