I n = ∫₀^(π /4) tan ⁿx dx then lim n → ∞ n[ I n + I n + 2 ] equals

Integral Calculus: JEE Main 2002 Mathematics question

JEE Main 2002 · Annual, Paper 1 · Q3324

JEE Main 2002Annual, Paper 1MathematicsMediumIntegral Calculus369× since 2002

{I_n} = \int\limits_0^{\pi /4} {{{\tan }^n}x\,dx}

then

\,\mathop {\lim }\limits_{n \to \infty } \,n\left[ {{I_n} + {I_{n + 2}}} \right]

equals

JEE Main 2002 · Annual, Paper 1 · Q3324

JEE Main 2002Annual, Paper 1MathematicsMediumIntegral Calculus369× since 2002

{I_n} = \int\limits_0^{\pi /4} {{{\tan }^n}x\,dx}

then

\,\mathop {\lim }\limits_{n \to \infty } \,n\left[ {{I_n} + {I_{n + 2}}} \right]

equals