1. Area, Antiderivatives, and Integrals
4.2
OBJECTIVES
Find an antiderivative of a function.
Evaluate indefinite integrals using the basic integration formulas.
Use initial conditions, or boundary conditions, to determine an antiderivative.

2. 4.2 Area, Antiderivatives, and Integrals
Antidifferentiate (find the antiderivative of) x2.

3. 4.2 Area, Antiderivatives, and Integrals
Integrals and Integration
Antidifferentiating is often called integration.
To indicate the antiderivative of x2 is x3/3 +C, we
write
where the notation
is used to represent the antiderivative of f (x).
More generally,
where
F(x) + C is the general form of the antiderivative of f (x).

4. 4.2 Area, Antiderivatives, and Integrals
Evaluate:
Evaluate:
Evaluate: a ) 7 e 6 x - ( ò d ; b 1 3 + 4 æ è ç ö ø ÷

5. 4.2 Area, Antiderivatives, and Integrals
Find the function f such that