Which of the following best describes the indefinite integral ?

Question

Which of the following best describes the indefinite integral  ?

BlackTom AI · Accepted Answer

The prompt asks: Which of the following best describes the indefinite integral ?

However, the provided answer options are not present in the input, so I can’t enumerate and evaluate each choice against the other possibilities.

From mathematical standard, the indefinite integral of f(x) with respect to x is defined as the family of antiderivatives of f. This means: if F is an antiderivative of f, then F'(x) = f(x) for all x in the domain, and the indefinite integral ∫ f(x) dx equals F(x) + C, where C is an arbitrary constant. In other words, it describes a family of differentiable functions, each of which has derivative equal to f(x).

Given the provided single option text in the input, 'A family of differentiable functions, each of which has derivative equal to f(x).', this matches the standard description of an indefinite integral as the set of all antiderivatives of f. Since other options are not listed here, it is not possible to compare alternatives, but the described concept is correct for the indefinite integral.

MATH_1225_17255_202501 5.4 Indefinite Integrals and the Net Change Theorem

Which of the following best describes the indefinite integral ?

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Question text Find [math: ∫2x4+3x3−3x+4]\displaystyle\int{2\,x^4+3\,x^3-3\,x+4} [math: dx]. Note: Type "[math: c]" for the integral constant. [input] Check Question 15

MTH1010_10_08_3

MTH1010_10_03_4

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