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Explain why the "+ C" is not needed in the antiderivative when evaluating a definite integral.

Sagot :

The reason the "+ C" is not needed in the antiderivative when evaluating a definite integral is; The C's cancel each other out as desired.

How to represent Integrals?

Let us say we want to estimate the definite integral;

I = [tex]\int\limits^a_b {f'(x)} \, dx[/tex]

Now, for any C, f(x) + C is an antiderivative of f′(x).

From fundamental theorem of Calculus, we can say that;

[tex]I = \int\limits^a_b {f'(x)} \, dx = \phi(a) - \phi(b)[/tex]

where Ф(x) is any antiderivative of f'(x). Thus, Ф(x) = f(x) + C would not work because the C's will cancel each other.

Read more about Integrals at; https://brainly.com/question/22008756

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