If $P = \mathop \smallint \nolimits_0^{3\pi } \,\,f\,\,({\cos ^2}\,\,x)\,\,dx\,\,{\rm{and}}\,\,{\cal Q} = \mathop \smallint \nolimits_0^\pi \,\,f({\cos ^2}\,\,x)\,\,dx$ , then

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

P = \int \nolimits_0^{3\pi } \,\,f\,\,({\cos ^2}\,\,x)\,\,dx\,\,\mathrm{and}\,\,{\cal Q} = \int \nolimits_0^\pi \,\,f({\cos ^2}\,\,x)\,\,dx

, then

View answer and explanation

Correct option: C

P\,\, - \,\,3\,{\cal Q} = 0

Option C (

P\,\, - \,\,3\,{\cal Q} = 0

) is correct because the integral from 0 to 3

\pi

of f(cos²x) is three times the integral from 0 to

\pi

of f(cos²x).

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