I’m currently operating with the following integral:
∫u′(t)(1−u(t))2dt
But I notice that
ddtu(t)1−u(t)=u′(t)(1−u(t))2
and
ddt11−u(t)=u′(t)(1−u(t))2
It seems that both solutions are possible, but that seems to contradict the uniqueness of Riemann’s Integral.
So the questions are:
- Which one of them is the correct integral?
- If both are correct, why the solution is not unique?
- The pole at u(t)=1 has something to say?
Answer
It is not really a contradiction, since difference of the two functions is constant:
11−u(t)−u(t)1−u(t)=1−u(t)1−u(t)=1.
(Derivative of a constant function is zero. Primitive function is determined uniquely up to a constant.)
Attribution
Source : Link , Question Author : Dargor , Answer Author : Martin Sleziak