Hi I feel very lost.

Question is if f is a differentiable function such that f(x) is never zero and

definite integral (I will use "S") b=x; a=0 f(t)dt = (f(x))^2 for all x, find f.

So my first thought is to let y = f(x) so S b=x; a=0 f(t) dt = y^2

then S b=x; a=0 2y = y^2 but I still don't have a clue what f is and if I jumped too far with the 2y

Please help. I can't find an example anywhere in my textbook on how to find f.

Thanks

This calculus beginner