设f(x)为连续函数,且满足∫(上x^3-1,下0)f(t)dt=x,则f(7)=
问题描述:
设f(x)为连续函数,且满足∫(上x^3-1,下0)f(t)dt=x,则f(7)=
答
g(x^3-1)-g(0)=x
y=x^3-1,得x=(y+1)^(1/3)
所以,g(y)=(y+1)^(1/3)+g(0)
f(y)=g'(y)=1/3(y+1)^(-2/3)
7带入.f(7)=1/12