Question Number 222754 by hardmath last updated on 06/Jul/25
Commented by hardmath last updated on 06/Jul/25
$$\int_{\mathrm{0}} ^{\:\mathrm{8}} \left(\mathrm{f}^{\:−\mathrm{1}} \left(\mathrm{x}\right)\:−\:\mathrm{f}\left(\mathrm{x}\right)\right)\:\mathrm{dx}\:=\:\mathrm{12} \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{8}} \:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:? \\ $$
Answered by mr W last updated on 07/Jul/25
$$\int_{\mathrm{0}} ^{\mathrm{8}} {f}\left({x}\right){dx}=\frac{\mathrm{8}×\mathrm{8}}{\mathrm{2}}−\frac{\mathrm{12}}{\mathrm{2}}=\mathrm{26} \\ $$
Commented by hardmath last updated on 07/Jul/25
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{dear}\:\mathrm{professor} \\ $$$$\mathrm{but}\:\mathrm{how}\:\mathrm{please} \\ $$
Commented by mr W last updated on 07/Jul/25
Commented by hardmath last updated on 07/Jul/25
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}\:\mathrm{my}\:\mathrm{dear}\:\mathrm{professor} \\ $$