If ${I_n} = \mathop \smallint \nolimits_0^{\pi /4} {\tan ^n}\,\,{\rm{\theta }}\;\,\,d{\rm{\theta }}$, then ${I_8} + {I_6}$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

{I_n} = \int \nolimits_0^{\pi /4} {\tan ^n}\,\,\mathrm{\theta }\;\,\,d\mathrm{\theta }

, then

{I_8} + {I_6}

is equal to

View answer and explanation

Correct option: A

\frac{1}{7}

The correct answer is A (

\frac{1}{7}

) because after applying the reduction formula and evaluating the definite integral, the result is

\frac{1}{7}

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