Let ${I_n} = \mathop \smallint \limits_0^{\pi /4} \,\,{\tan ^n}x\,\,dx,\,\,\left( {n > 1\,\,{\rm{and}}\,\,n \in N} \right)$, then

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

Let

{I_n} = \int \limits_0^{\pi /4} \,\,{\tan ^n}x\,\,dx,\,\,\left( {n > 1\,\,\mathrm{and}\,\,n \in N} \right)

, then

View answer and explanation

Correct option: B

{I_n}\,\, + \,\,{I_{n - 2}} = \,\,\frac{1}{{n - 1}}

Option B is correct because the recurrence relation between In and In-2 is found to be

{I_n}\,\,+ \,{I_{n - 2}} = \,\,\frac{1}{{n - 1}}

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