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Techniques of Integration: Integration by Substitution and Integration by Parts, Lecture notes of Statistics

University of Botswana Statistics

Differential EquationsReal AnalysisVector calculus

This chapter covers two techniques for finding indefinite integrals: integration by substitution and integration by parts. The former is used when the integral can be transformed into the derivative of a known function, while the latter is used when the integral can be expressed as the product of two functions. Examples and solutions for each technique.

What you will learn

How do you find the indefinite integral of a function using Integration by Substitution?
Can you provide an example of how to use Integration by Parts to find the indefinite integral of a function?
What is the formula for Integration by Parts and how is it used?

Typology: Lecture notes

2021/2022

Uploaded on 01/28/2022

tmkgomotso 🇧🇼

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Partial preview of the text

Download Techniques of Integration: Integration by Substitution and Integration by Parts and more Lecture notes Statistics in PDF only on Docsity! Chapter 6 - Techniques of Integration 6.1 Integration by Substitution We know that the derivative of a function is obtained by the Chain rule: , that is let , then . Therefore, if we have a function of the form , then the indefinite integral (anti-derivative) is , that is . Example 6.1.1 Find . Solution 6.1.1 Put . Therefore, this implies that . Example 6.1.2 (i) Evaluate (i) and (ii) . Solution 6.1.2 (i) Put . Therefore, this implies that = . (ii) Example 6.1.3

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