4 1 Antiderivatives and Indefinite Integration Part I

4. 1: Antiderivatives and Indefinite Integration (Part I) Greg Kelly, Hanford High School, Richland, Washington

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

Suppose we have a function F whose derivative is 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.

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.

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

Notation: variable of integration integrand constant of integration 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.

Basic Integration Rules: Integration and differentiation are inverse processes.

Look at basic integration rules on page 244. Integration Differentiation

Look at basic integration rules on page 244. Integration Differentiation

Examples:

Examples:

Examples:

Homework 4. 1 (page 249) #1 -41 odd