设f(x)是以l为周期的连续函数,证明§a,a+l f(x)dx与a无关
问题描述：
设f(x)是以l为周期的连续函数,证明§a,a+l f(x)dx与a无关
答
f(x)是以l为周期的连续函数=> f(x+l) = f(x)I= ∫(a,a+l) f(x)dxlet F(x) = ∫ f(x)dxI = F(a+l) - F(a)dI/da = F'(a+l) - F'(a)= f(a+l) - f(a)= f(a) - f(a) =0dI/da =0=> I is independent of a