Question

12. If f(x) is defined in (0,2π), then an, is

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Answer 1

$a_0=\frac{1}{p}{\int}^{2p}_0 x\sin xdx\\\\=\frac{1}{p}[x(-\cos x)+\int\cos\:x.1dx]\\\\=\frac{1}{p}[-x\cos x+0\sin x{]}^{2p}_0\\\\= -2$