If $\mathop \smallint \limits_0^{\pi /2} {\cos ^n}\,\,x\,\,{\sin ^n}\,\,x\,dx = \lambda \,\mathop \smallint \limits_0^{\pi /2} {\sin ^n}\,\,x\,dx$, then $\lambda = $

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

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

, then

\lambda =

View answer and explanation

Correct option: C

\frac{1}{{{2^n}}}

Option C (

\frac{1}{{{2^n}}}

) is correct because after applying trigonometric identities and properties of definite integrals, the value of

\lambda

is found to be

\frac{1}{{{2^n}}}

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