A Symmetry Worth Ten
Difficulty: Medium · Topics: Calculus, Integration, Definite Integrals
O‘nga arziydigan simmetriya
A continuous function f(x) defined on the closed interval ≤ft[0,\ (π)/(2) ] satisfies f(x)=f≤ft((π)/(2)-x ).
If ∫ 0^(π)/(2)f(x)cos^2x dx=10, find the value of ∫ 0^(π)/(2)f(x) dx.
≤ft[0,\ (π)/(2) ] yopiq oraliqda aniqlangan uzluksiz f(x) funksiya f(x)=f≤ft((π)/(2)-x ) ni qanoatlantiradi.
Agar ∫ 0^(π)/(2)f(x)cos^2x dx=10 bo‘lsa, ∫ 0^(π)/(2)f(x) dx ning qiymatini toping.