Integration by Substitution

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# Integration by Substitution - PowerPoint PPT Presentation

## Integration by Substitution

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##### Presentation Transcript

1. Integration by Substitution If you cannot see the answer for integral by inspection, then the method of substitution is deployed. Example 1 Make dx the subject Replace 2x – 1 by u and write dx in terms of du This was an easy question, you could have done it by inspection.

2. Integration by substitution Example 2 Use the substitution u = sin x Make dx the subject This was also an easy question, you could have done it by inspection.

3. Integration by substitution Integrals which are not so obvious. Example 3 Use the substitution u = x - 4 However, this integral can be found by using partial fractions.

4. Integration by substitution Substitute x = u2 Example 4

5. Integration by substitution Example 5 Substitute u2 = x + 1

6. Integration by substitution Example 6 Substitute x = (u – 4)/3

7. Integration by substitution Substitute x = 2sin u Example 7