Whutever42
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I'm currently taking a Calc I class and we just learned the term "Anti-Derivative". I was confused by this and just wanted some clarification on what the term means. Thank you! ;-)
What is an anti-derivative?
- Thread starter Whutever42
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mmm4444bot
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If you google keyword antiderivative, you'll find lots of sites providing the definition and examples (written explanations, as well as video lectures). I would also encourage you to check your textbook's index, as well as looking for a glossary, for additional insight.
In short, an antiderivative of a function f(x) is a differentiable function F(x) whose first derivative is f(x).
Given: f(x) = x^2
Antiderivative: F(x) = 1/3 x^3 + C (where C is an arbitrary constant) because F'(x) = f(x).
Due to the constant C, we see that f(x) has an infinite family of antiderivatives. :cool:
In short, an antiderivative of a function f(x) is a differentiable function F(x) whose first derivative is f(x).
Given: f(x) = x^2
Antiderivative: F(x) = 1/3 x^3 + C (where C is an arbitrary constant) because F'(x) = f(x).
Due to the constant C, we see that f(x) has an infinite family of antiderivatives. :cool: