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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