If ${I_n} = \mathop \smallint \limits_0^{\pi /4} {\tan ^n}\,\,x\,\,dx$, then $\mathop {\lim }\limits_{n \to \infty } \,\,n\,\,\left( {{I_{n + 1}}\,\, + \,\,{I_{n - 1}}} \right)$ equals

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

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

, then

\lim\limits_{n \to \infty } \,\,n\,\,\left( {{I_{n + 1}}\,\, + \,\,{I_{n - 1}}} \right)

equals

View answer and explanation

Correct option: A

Option A (1) is correct because the limit simplifies to 1 by using the recurrence relation In+1 + In-1 = 1/n.

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