Integrals

Calculus Level 4

Let \(f(x)=\dfrac{1}{2}a_0+\displaystyle\sum_{i=1}^n a_i \cos(ix)+\displaystyle\sum_{j=1}^nb_j \sin(jx)\), then \(\displaystyle\int_{-\pi}^{\pi} f(x) \cos (kx) \, dx\) (where \(k \leq n\)) is equal to which of the following?

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