jee-main 2022 Q73

jee-main · India · session2_28jul_shift2 Reduction Formulae Derive a Reduction/Recurrence Formula via Integration by Parts

Let $I _ { n } ( x ) = \int _ { 0 } ^ { x } \frac { 1 } { \left( t ^ { 2 } + 5 \right) ^ { n } } d t , n = 1,2,3 , \ldots$. Then
(1) $50 I _ { 6 } - 9 I _ { 5 } = x I _ { 5 } ^ { \prime }$
(2) $50 I _ { 6 } - 11 I _ { 5 } = x I _ { 5 } ^ { \prime }$
(3) $50 I _ { 6 } - 9 I _ { 5 } = I _ { 5 } ^ { \prime }$
(4) $50 I _ { 6 } - 11 I _ { 5 } = I _ { 5 } ^ { \prime }$

Let $I _ { n } ( x ) = \int _ { 0 } ^ { x } \frac { 1 } { \left( t ^ { 2 } + 5 \right) ^ { n } } d t , n = 1,2,3 , \ldots$. Then\\
(1) $50 I _ { 6 } - 9 I _ { 5 } = x I _ { 5 } ^ { \prime }$\\
(2) $50 I _ { 6 } - 11 I _ { 5 } = x I _ { 5 } ^ { \prime }$\\
(3) $50 I _ { 6 } - 9 I _ { 5 } = I _ { 5 } ^ { \prime }$\\
(4) $50 I _ { 6 } - 11 I _ { 5 } = I _ { 5 } ^ { \prime }$

Paper Questions

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