If ${u_n} = \mathop \smallint \nolimits_0^{\pi /4} {\tan ^n}\,\,x\,dx,$, then ${u_n}\,\, + \,\,{u_{n - 2}}$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

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

, then

{u_n}\,\, + \,\,{u_{n - 2}}

is equal to

View answer and explanation

Correct option: A

\frac{1}{{n\,\, - \,\,1}}

Option A (

\frac{1}{{n\, - \,1}}

) is correct because by using integration by parts and simplifying, the expression

{u_n}\, + \,{u_{n - 2}}

simplifies to

\frac{1}{{n\, - \,1}}

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