Is the system $y(t)= dx(t)/dt$ invertible or not? If yes, please determine the inverse system for it.
It is not. It suffices to find a counter example. Let me tell you that "I am flat". Could you derive my actual value?
So, any constant function $f(t) =c$ is differentiable, and have the same derivative, $f'(t)=0$. Only from knowing that $f'(t)=0$, you cannot recover the original (constant) function. Hence the system is not invertible.
Delta coding (with no quantization) is quite close to what you are asking. Let:
x=randi([0 10], 8,1); delta = diff([0; x]); x_hat = cumsum(delta); assert(all(x-x_hat)==0);
But then you have a «silent agreement» to preprepend a zero such that you have a known starting point. And differentiation/integration is replaced by its discrete equivalents.