given-f-x-f-x-pi-6-x-R-if-0-pi-6-f-x-dx-T-then-pi-7pi-3-f-x-pi-dx-

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

g i v e n f (x) = f (x + \frac{π}{6}) \forall x \in R

i f \underset{0}{\int^{π / 6}} f (x) d x = T t h e n \underset{π}{\int^{7 π / 3}} f (x + π)

d x ?

Answered by bramlex last updated on 15/Jul/20

\Rightarrow \underset{π}{\int^{7 π / 3}} f (x + π) dx = \underset{0}{\int^{4 π / 3}} f (x) dx =

\underset{0}{\int^{8 (\frac{π}{6})}} f (x) dx = 8 T

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