设F(x)为f(x)的原函数,且F(x)=0.F(x)f(x)=sin2x的平方,F(x)大于等于0,求f(x).

令y=F(x)
f(x)=y'=dy/dx
F(x)f(x)=y*dy/dx=(sin2x)^2
ydy=(sin2x)^2dx
∫ydy=∫(sin2x)^2dx=∫(1-cos4x)/2 dx
(1/2)y^2=(1/2)[x-(1/4)sin4x]+C
y=√[x-(1/4)sin4x+C]
f(x)=sin2x/F(x)=sin2x/√[x-(1/4)sin4x+C]