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The question asks about the relationship between the antiderivative and the indefinite integral of a function. The correct answer is:

**a. La antiderivada y la integral indefinida son lo mismo y pueden usarse indistintamente.**

Explanation:
- The **antiderivative** of a function \( f(x) \) is a function \( F(x) \) such that \( F'(x) = f(x) \).
- The **indefinite integral** is essentially the same concept as the antiderivative but written in integral notation: \( \int f(x) \, dx = F(x) + C \), where \( C \) is a constant.
- Thus, they represent the same mathematical concept and can be used interchangeably.

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Here are 5 related questions to expand on this concept:
1. What is the difference between a definite and an indefinite integral?
2. How do you compute the antiderivative of a function?
3. What role does the constant \( C \) play in indefinite integrals?
4. Can every function have an antiderivative?
5. How is the process of finding an antiderivative different from solving a differential equation?

**Tip:** The constant \( C \) in indefinite integrals accounts for all possible vertical shifts of the antiderivative, ensuring that every solution is included.

Indica la relación que existe entre la antiderivada y la integral indefinida de una función, selecciona la opción que describe correctamente esta relación.

Explore the connection between antiderivatives and indefinite integrals in calculus. Learn why these concepts can be used interchangeably, their definitions, key formulas, and relevant theorems. Suitable for students in Grades 11-12 or early university level.

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