JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

Q(x)=\frac{1}{2} a_0+a_1 \cos x+b_1 \sin x+a_2 \cos 2 x

+\ldots+a_n \cos n x+b_n \sin n x

, then the value of

\int\limits_{0}^{2 \pi} Q(x) \sin k x \mathrm{~d} x(k=1,2, \ldots n)

View answer and explanation

Correct option: D

\pi b_k

Option D (

\pi b_k

) is correct because when integrating

Q(x) \sin kx

, only the term

b_k \sin kx \sin kx

contributes a non-zero value, resulting in

\pi b_k

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