Question

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

Answer 1

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 = $\int\limits^a_b {f'(x)} \, dx$

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

From fundamental theorem of Calculus, we can say that;

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

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; brainly.com/question/22008756

#SPJ1