Let ${I_n} = \mathop \smallint \limits_0^{\pi /2} \,\,{\cos ^n}\,x\,\,\,\cos \,\,n\,\,\,x\,\,dx$. Then, ${I_n}\,\,:\,\,{I_{n + 1}}$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

Let

{I_n} = \int \limits_0^{\pi /2} \,\,{\cos ^n}\,x\,\,\,\cos \,\,n\,\,\,x\,\,dx

. Then,

{I_n}\,\,:\,\,{I_{n + 1}}

is equal to

View answer and explanation

Correct option: C

\mathrm{2 : 1}

Option C (2 : 1) is correct because the ratio

{I_n}\,:\,{I_{n + 1}}

simplifies to 2:1 after applying trigonometric identities and integration by parts.

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