jee-main 2023 Q81

jee-main · India · session1_25jan_shift1 Integration by Substitution Substitution to Compute an Indefinite Integral with Initial Condition

Let $f ( x ) = \int \frac { 2 x } { \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } + 3 \right) } d x$. If $f ( 3 ) = \frac { 1 } { 2 } \left( \log _ { e } 5 - \log _ { e } 6 \right)$, then $f ( 4 )$ is equal to
(1) $\frac { 1 } { 2 } \left( \log _ { e } 17 - \log _ { e } 19 \right)$
(2) $\log _ { \mathrm { e } } 17 - \log _ { \mathrm { e } } 18$
(3) $\frac { 1 } { 2 } \left( \log _ { e } 19 - \log _ { e } 17 \right)$
(4) $\log _ { e } 19 - \log _ { e } 20$

Let $f ( x ) = \int \frac { 2 x } { \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } + 3 \right) } d x$. If $f ( 3 ) = \frac { 1 } { 2 } \left( \log _ { e } 5 - \log _ { e } 6 \right)$, then $f ( 4 )$ is equal to\\
(1) $\frac { 1 } { 2 } \left( \log _ { e } 17 - \log _ { e } 19 \right)$\\
(2) $\log _ { \mathrm { e } } 17 - \log _ { \mathrm { e } } 18$\\
(3) $\frac { 1 } { 2 } \left( \log _ { e } 19 - \log _ { e } 17 \right)$\\
(4) $\log _ { e } 19 - \log _ { e } 20$

Paper Questions

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