Problem

True or false: When using the Evaluation Theorem, we choose the antiderivative with $C=0$ because any other antiderivative will give a different answer.
True
False

Answer

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Answer

\(\boxed{\text{False}}\)

Steps

Step 1 :The Evaluation Theorem, also known as the Fundamental Theorem of Calculus, states that if a function is continuous over the interval [a, b] and F is an antiderivative of f on [a, b], then the definite integral of f from a to b is F(b) - F(a).

Step 2 :The constant of integration, C, arises when we find the indefinite integral of a function. However, when we are evaluating a definite integral, the constant of integration cancels out because we are finding the difference F(b) - F(a).

Step 3 :Therefore, it doesn't matter what value we choose for C when using the Evaluation Theorem, because it will not affect the final answer.

Step 4 :\(\boxed{\text{False}}\)

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