1. The Indefinite Integral

2. Antiderivative
An antiderivative of a function f is a function F such that
Ex.
An antiderivative of is
since

3. Indefinite Integral The expression:
read “the indefinite integral of f with respect to x,”
means to find the set of all antiderivatives of f.
x is called the variable of integration
Integrand
Integral sign

4. Constant of Integration
Every antiderivative F of f must be of the form F(x) = G(x) + C, where C is a constant.
Notice
Represents every possible antiderivative of 6x.

5. Power Rule for the Indefinite Integral, Part I
Ex.

6. Power Rule for the Indefinite Integral, Part II
Indefinite Integral of ex and bx

7. Sum and Difference Rules
Ex.
Constant Multiple Rule
Ex.

8. Integral Example/Different Variable
Ex. Find the indefinite integral:
Copyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc.

9. Position, Velocity, and Acceleration Derivative Form
If s = s(t) is the position function of an object at time t, then
Velocity = v =
Acceleration = a =
Integral Form

10. Copyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc.