If ${I_1} = \mathop \smallint \limits_0^{3\pi } \,\,f\left( {{{\cos }^2}\,\,x} \right)\,dx$ and ${I_2} = \mathop \smallint \limits_0^\pi \,\,f\left( {{{\cos }^2}\,\,x} \right)\,\,dx$ then

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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{I_1} = \int \limits_0^{3\pi } \,\,f\left( {{{\cos }^2}\,\,x} \right)\,dx

and

{I_2} = \int \limits_0^\pi \,\,f\left( {{{\cos }^2}\,\,x} \right)\,\,dx

then

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Correct option: D

None of these

Option D (None of these) is correct because

{I_1} = 3{I_2}

, which is not represented by options A, B, or C.

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