If ${I_1} = \mathop \smallint \nolimits_0^{3\pi } \,\,f\,\,({\cos ^2}\,\,x)\,\,dx$ and ${I_2} = \mathop \smallint \nolimits_0^\pi \,\,f({\cos ^2}\,\,x)\,\,dx,{\rm{then}}$,〗 then

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

{I_1} = \int \nolimits_0^{3\pi } \,\,f\,\,({\cos ^2}\,\,x)\,\,dx

and

{I_2} = \int \nolimits_0^\pi \,\,f({\cos ^2}\,\,x)\,\,dx,\mathrm{then}

,〗 then

View answer and explanation

Correct option: C

{I_1} = 3\,{I_2}

Option C (

{I_1} = 3\,{I_2}

) is correct because the integral

{I_1}

can be split into three equal integrals, each equal to

{I_2}

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