f(x)在[0,1]连续,f(x)=3x-√(1-x^2)[∫f^2(x)]dx,求f(x)
问题描述：
f(x)在[0,1]连续,f(x)=3x-√(1-x^2)[∫f^2(x)]dx,求f(x)
答
f^2(x)是f(x)的平方还是二阶导数?如果是平方:令k=∫[f(x)]^2dx则f(x)=3x-k√(1-x^2)[f(x)]^2=k^2+(9-k^2)x^2-6kx√(1-x^2)k=∫[f(x)]^2dx=∫[k^2+(9-k^2)x^2-6kx√(1-x^2)]dx=k^2+(9-k^2)∫x^2dx-6k∫x√(1-x^2)dx=k...