设连续函数fx满足fx=x∧2-∫1-0 fxdx,求fx

2024-12-27 18:58:00
推荐回答(1个)
回答1:

f(x)=x^2-∫(0->1) f(x)dx
let
f(x) =x^2+ C

x^2-∫(0->1) f(x)dx
=x^2-∫(0->1) (x^2+C)dx
=x^2 - [(1/3)x^3+ Cx]|(0->1)
=x^2 - (1/3+ C )
=>
C= -(1/3+C)
C= -1/6

f(x) = x^2 -1/6