1. and Indefinite Integration (Part I)
4.1: Antiderivatives
and Indefinite Integration (Part I)
Greg Kelly, Hanford High School, Richland, Washington

2. Objectives Write the general solution of a differential equation.
Use indefinite integral notation for antiderivatives.
Use basic integration rules to find antiderivatives.

3. Suppose we have a function F whose derivative is
 an antiderivative of f
 an antiderivative of f
 an antiderivative of f
So we can say:
We don’t know what the constant is, so we put “C” in the answer to remind us that there might have been a constant.

4. A differential equation in x and y is an equation that involves x, y, and derivatives of y.
For example:
are examples of differential equations.

5. Find the general solution of the differential equation
(Find a function whose derivative is 2.)

6. Notation:
variable of integration
constant of integration
integrand
Antiderivative of f with respect to x
The differential dx serves to identify x as the variable of integration.
Indefinite integral is a synonym for antiderivative.

7. Basic Integration Rules:
Integration and differentiation are inverse processes.

8. Look at basic integration rules on page 244.
Differentiation

9. Look at basic integration rules on page 244.
Differentiation

10. Examples:

11. Examples:

12. Examples:

13. Homework
4.1 (page 249)
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