f(x)=x^2-∫(0到a)f(x)dx,a为常数且不等于-1,证f(0)=-a^3/3(a+1)

问题描述:

f(x)=x^2-∫(0到a)f(x)dx,a为常数且不等于-1,证f(0)=-a^3/3(a+1)

f'(x)=2x f(x)=x^2+c
f(x)=x^2-(1/3)a^3-ac
c=-(1/3)a^3-ac
c=-a^3/3(a+1)
f(0)=-a^3/3(a+1)