jee-main 2021 Q75

jee-main · India · session3_20jul_shift2 Indefinite & Definite Integrals Integral Equation with Symmetry or Substitution

Let $g ( t ) = \int _ { - \pi / 2 } ^ { \pi / 2 } \left( \cos \frac { \pi } { 4 } t + f ( x ) \right) d x$, where $f ( x ) = \log _ { e } \left( x + \sqrt { x ^ { 2 } + 1 } \right) , x \in R$. Then which one of the following is correct?
(1) $g ( 1 ) = g ( 0 )$
(2) $\sqrt { 2 } g ( 1 ) = g ( 0 )$
(3) $g ( 1 ) = \sqrt { 2 } g ( 0 )$
(4) $g ( 1 ) + g ( 0 ) = 0$

Let $g ( t ) = \int _ { - \pi / 2 } ^ { \pi / 2 } \left( \cos \frac { \pi } { 4 } t + f ( x ) \right) d x$, where $f ( x ) = \log _ { e } \left( x + \sqrt { x ^ { 2 } + 1 } \right) , x \in R$. Then which one of the following is correct?\\
(1) $g ( 1 ) = g ( 0 )$\\
(2) $\sqrt { 2 } g ( 1 ) = g ( 0 )$\\
(3) $g ( 1 ) = \sqrt { 2 } g ( 0 )$\\
(4) $g ( 1 ) + g ( 0 ) = 0$

Paper Questions

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