Definite Integration

JEE Main 2002 · Annual, Paper 1 · Q3324

MathematicsMedium210×since 2002Q3324

{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

MathematicsMedium210×since 2002Q3324

{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

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