Final answer:
The truth set for the predicate P(x): x² = 2 within the domain of integers is the empty set, as no integer solutions fulfill this equation.
Step-by-step explanation:
The predicate given is P(x): x² = 2. Since we are looking for the truth set within the domain of integers, we must search for integer values of 'x' that satisfy the equation. In this case, there are no integers that square to 2, which is a known irrational number. Thus, the truth set is an empty set.
The provided references to completing the square or finding areas under functions are not directly relevant to solving the initial equation x² = 2 for integer solutions.