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6.1: Antiderivatives and Indefinite Integrals

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1 6.1: Antiderivatives and Indefinite Integrals

2 Determine the Function
You are given a function where What is the function f(x)? This process of determining the original function from its derivative is known as antidifferentiation.

3 A function F is an antiderivative of a function f if for every x in the domain of f, .
If F(x) is an antiderivative of f(x), then F(x) + C is also an antiderivative of f(x). Antidifferentiation determines a family of functions.

4 Notation Integrand Antiderivative Integral sign Differential

5 Examples: Rewrite using integral notation

6 How are Differentiation and Integration related?

7 Basic Integration Rules

8 Examples

9 More Examples

10 Particular Solutions Finding C, we are solving a differential equation. Ex: Find a general solution of , and find the particular solution that satisfies F(1) = 8.

11 Applications Checkpoint 8, p. 370 Checkpoint 9, p. 371

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