Question

高等数学，大神求解一下

越详细越好，感谢

Answer 1

f(x)=-f(x)
f(0)=0
f(x T)=f(x)
S(0，T)f(t)dt= (let u =-t) s (0，-t) f (-u) d (-u) = s (0，-t) f (u) du = (let v = u t) s (t，0) f(。
S(0，T)f(t)dt=0
F(-x)=S(0，-x)f(t)dt= (let u =-t) s (0，x) f (-u) d (-u) = s (0，x) f (u) du = f (x)偶函数
F (x t) = s (0，x t) f (t) dt = s (0，t) f (t) dt s (t，x t) f (t) dt = s (t，x t) f (t) dt = (let u = t-t) s (t)