Calculus I

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Antiderivative

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Calculus I

Definition

An antiderivative of a function $f(x)$ is another function $F(x)$ such that the derivative of $F(x)$ is equal to $f(x)$. It is also known as the indefinite integral of $f(x)$.

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5 Must Know Facts For Your Next Test

  1. The process of finding an antiderivative is called integration.
  2. Antiderivatives are determined up to an arbitrary constant, often denoted as $C$.
  3. If $F(x)$ is an antderivative of $f(x)$, then every antiderivative of $f(x)$ can be written as $F(x) + C$.
  4. Common functions have standard antiderivatives, such as $\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$ for any real number n ≠ -1.
  5. To check if a function is an antiderivative, differentiate it and see if you get back the original function.

Review Questions

  • What is the relationship between a function and its antiderivative?
  • Explain why every antiderivative includes an arbitrary constant.
  • How would you find the antiderivative of a polynomial function?
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