Final answer:
The correct rule for combining definite integrals is the Additivity rule, which allows the addition or subtraction of integrals with the same limits by summing their integrands.
Step-by-step explanation:
The rule used for combining definite integrals is the Additivity rule. This rule states that if you have two definite integrals with the same variable of integration and the same limits of integration, you can combine them by simply adding or subtracting the integrands, depending on the operation between the two integrals. For example, if you are given ∫a to ∫b of f(x) dx and ∫a to ∫b of g(x) dx, you can add these two integrals to get ∫a to ∫b of (f(x) + g(x)) dx.
This principle also applies in a broader sense, reflecting the linearity property of integrals. If the integrands are multiplied by constants, or if there are multiple terms in the integrand that could be integrated separately, the integrals can be combined or separated accordingly. This property is crucial for simplifying complex integration problems and utilizing the principle of superposition when dealing with functions that are sums of simpler functions.
Therefore, the correct option for combining definite integrals is the Additivity rule, making the answer to the student's question C) Additivity rule.