The value of $\mathop \smallint \nolimits_0^\pi \,\,\left( {\mathop \sum \nolimits_{r = 0}^3 \,\,{a_r}\,{{\cos }^{3 - r}}\,\,x\,\,{{\sin }^r}\,\,x} \right)dx$ depends upon

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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The value of

\int \nolimits_0^\pi \,\,\left( {\sum \nolimits_{r = 0}^3 \,\,{a_r}\,{{\cos }^{3 - r}}\,\,x\,\,{{\sin }^r}\,\,x} \right)dx

depends upon

View answer and explanation

Correct option: D

{a_1}

and

{a_3}

Option D (

{a_1}

and

{a_3}

) is correct because only the integrals involving

\cos^2 x \sin x

and

\sin^3 x

are non-zero over the interval

[0, \pi]

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