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Given-that-f-x-f-x-1000-for-every-x-R-If-0-3-f-x-30-what-is-the-value-of-3-5-f-x-2016-dx-




Question Number 10849 by Joel576 last updated on 27/Feb/17
Given that f(x) = f(x + 1000) for every x ∈ R  If ∫_0 ^3  f(x) = 30,what is the value of  ∫_3 ^5  f(x + 2016) dx ?
$$\mathrm{Given}\:\mathrm{that}\:{f}\left({x}\right)\:=\:{f}\left({x}\:+\:\mathrm{1000}\right)\:\mathrm{for}\:\mathrm{every}\:{x}\:\in\:\mathbb{R} \\ $$$$\mathrm{If}\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:{f}\left({x}\right)\:=\:\mathrm{30},\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\underset{\mathrm{3}} {\overset{\mathrm{5}} {\int}}\:{f}\left({x}\:+\:\mathrm{2016}\right)\:{dx}\:? \\ $$

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