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Some Rules for Integration

Example 1

Evaluate

Solution : Using rule 2, we find that

Also, using formula ( 1 ), we get


Example 2

Evaluate

Solution : Using rule 2 and formula (4), we get

Example 3

Evaluate

Solution :

Example 4

Evaluate

Solution :

using rules 1, 2 and applying standard results (1), (2), we get

Example 5

Evaluate

Solution :

using (22), with a2 = 49, we get

Example 6

Solution :

applying (24), we get

Example 7

   Evaluate

Solution :

By rule (1) and (2), we have

Using standard results (1), (4), (13) and (11) respectively, you find

Example 9

Integrate w. r. to x. the following

Solution :

Using (1), (3), (4), (5) and again (1) respectively we get

Example 10

Integrate w. r. to. x, the following

Solution :

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Index

6.1 Anti-derivatives (indefinite Integral)
6.2 Integration Of Some Trignometric Functions
6.3 Methods Of Integration
6.4 Substitution And Change Of Variables
6.5 Some Standard Substitutions
6.6 Integration By Parts
6.7 Integration By Partial Fractions

Chapter 7





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