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comment Prove $\forall \delta >0, \, \exists C>0 \, \,s.t.\, |\int_{x}^{\pi}D_n(t)\, dt| \leq \frac{C}{n}$. (Dirichlet kernel)
Well, I think the author probably meant $x \in [\delta,\pi]$. Just another typo. I only needed this to prove the Dirichlet-Jordan theorem, but what i have shown in my first answer is enough to do so. I hope this helps somebody someday.
Oct
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answered Prove $\forall \delta >0, \, \exists C>0 \, \,s.t.\, |\int_{x}^{\pi}D_n(t)\, dt| \leq \frac{C}{n}$. (Dirichlet kernel)