${I_n} = \mathop \smallint \nolimits_0^{\pi /4} \,\,{\tan ^n}\,\,x\,\,dx$, then $\mathop {\lim }\limits_{n \to \infty } n\,\,\left[ {{I_n}\,\, + \,\,{I_{n + 2}}} \right]$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

{I_n} = \int \nolimits_0^{\pi /4} \,\,{\tan ^n}\,\,x\,\,dx

, then

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

is equal to

View answer and explanation

Correct option: B

\mathrm{1}

Option B (

\mathrm{1}

) is correct because the limit is evaluated by simplifying the integral and applying the limit definition.

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