Question Number 89745 by jagoll last updated on 19/Apr/20
$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{f}\left(\mathrm{x}+\frac{\mathrm{3}\pi}{\mathrm{8}}\right)\:,\:\forall\mathrm{x}\in\:\mathbb{R} \\ $$$$\mathrm{if}\:\underset{\mathrm{0}} {\overset{\mathrm{3}\pi/\mathrm{8}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{t}\:,\:\mathrm{then}\: \\ $$$$\underset{\pi} {\overset{\mathrm{5}\pi/\mathrm{2}} {\int}}\mathrm{f}\left(\mathrm{x}−\pi\right)\:\mathrm{dx}\:=\: \\ $$$$\mathrm{A}.\:\mathrm{2t}\:\:\:\:\:\:\:\mathrm{B}.\:\mathrm{3t}\:\:\:\:\:\:\:\mathrm{C}.\:\mathrm{4t}\:\:\:\:\:\:\:\mathrm{D}.\:\mathrm{6t} \\ $$$$\mathrm{E}.\:\mathrm{8t}\: \\ $$
Commented by john santu last updated on 19/Apr/20
$$\underset{\pi\:−\pi} {\overset{\frac{\mathrm{5}\pi}{\mathrm{2}}\:−\pi} {\int}}{f}\left({x}\right)\:{dx}\:=\:\underset{\mathrm{0}} {\overset{\frac{\mathrm{3}\pi}{\mathrm{2}}} {\int}}\:{f}\left({x}\right)\:{dx}\:= \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{4}×\frac{\mathrm{3}\pi}{\mathrm{8}}} {\int}}{f}\left({x}\right)\:{dx}\:=\:\mathrm{4}{t}\: \\ $$
Commented by jagoll last updated on 19/Apr/20
$$\mathrm{yes} \\ $$