Suppose f(x) is a continuous function. Then a function F(x) such that F'(x) = f(x) is called:
A.) the indefinite integral of f
B.) the antiderivative of f
C.) an antiderivative of f
D.) a definite integral of f
E.) All of the above
The answer is C! AN antiderivative of f
The correct answer is C) an antiderivative of f.
An antiderivative of a function f(x) is a function F(x) whose derivative is equal to f(x). In other words, if F'(x) = f(x), then F(x) is an antiderivative of f(x).
Option A) the indefinite integral of f, refers to a family of antiderivatives of f(x). The indefinite integral is denoted using the integral symbol ∫ and does not have any specific limits of integration.
Option D) a definite integral of f, refers to the evaluation of the integral of f(x) over a specific interval. It does not represent an antiderivative.
Therefore, option C) an antiderivative of f, is the correct choice since it accurately describes a function F(x) whose derivative is f(x).