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Question Number 103515 by bemath last updated on 15/Jul/20

$$givenf\left(x\right)=f(x+\frac{\pi }{6})\mathrm{\forall }x\in \mathbb{R}$$$$if\underset{0}{\stackrel{\pi /6}{\int }}f\left(x\right)dx=Tthen\underset{\pi }{\stackrel{7\pi /3}{\int }}f(x+\pi )$$$$dx?$$

Answered by bramlex last updated on 15/Jul/20

$$\Rightarrow \underset{\pi }{\stackrel{7\pi /3}{\int }}\mathrm{f}(\mathrm{x}+\pi )\mathrm{dx}=\underset{0}{\stackrel{4\pi /3}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=$$$$\underset{0}{\stackrel{8\left(\frac{\pi }{6}\right)}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=8\mathrm{T}◼$$

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