Antidifferentiation by Substitution

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6.2 Antidifferentiation by Substitution
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Presentation transcript:

Antidifferentiation by Substitution Chapter 7 Differential Equations and Mathematical Modeling Section 7.2 Antidifferentiation by Substitution

What you’ll learn about Indefinite integrals Properties of indefinite integrals Antiderivative formulas arising from known derivatives Leibniz notation (differentials) in integrals Using substitution to evaluate indefinite integrals Using substitution to evaluate definite integrals … and why Antidifferentiation techniques were historically crucial for applying the results of calculus.

Indefinite Integral

Example Evaluating an Indefinite Integral

Properties of Indefinite Integrals

Power Functions

Trigonometric Formulas

Exponential and Logarithmic Formulas

Example Paying Attention to the Differential  

Example Using Substitution

Example Using Substitution

Example Setting Up a Substitution with a Trigonometric Identity

Example Evaluating a Definite Integral by Substitution

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