If $\mathop \smallint \limits_0^{n{\rm{ }}\pi } \,\,f\left( {{{\cos }^2}\,\,x} \right)\,\,dx = k\,\,\mathop \smallint \limits_0^\pi \,\,f\left( {{{\cos }^2}\,\,x} \right)\,\,dx$, then the value of $k$, is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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\int \limits_0^{n\mathrm{ }\pi } \,\,f\left( {{{\cos }^2}\,\,x} \right)\,\,dx = k\,\,\int \limits_0^\pi \,\,f\left( {{{\cos }^2}\,\,x} \right)\,\,dx

, then the value of

k

, is

View answer and explanation

Correct option: B

n

Option B is correct because the integral of a periodic function over n periods is n times the integral over one period.

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