CONSTRUCTING ANTIDERIVATIVES ANALYTICALLY
CONSTRUCTING ANTIDERIVATIVES ANALYTICALLY
1. If a function [pic] that is has a family of antidervatives of the form [pic].
a. We use a notation for the general antidervative that looks like the definite integral without the limits and it called the indefinite integral.
[pic].
2. It is important to understand the difference between the following:
a. [pic] This is a number
b. [pic] This is a family of functions
Types of Antidervatives:
1) What is an antiderivative of [pic]
a) Then [pic]
2) What is the antidervative of [pic]
a) [pic]
3) What is the antidervative of a power of x?
a) [pic]
b) Example: What is the antidervative of [pic] Answer: [pic]
c) What if [pic]See number 4.
4) What is the antiderivative of [pic]?
a) [pic] if [pic].
b) [pic] ( because ln is not defined for x1.
b=7
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