Contents

6.1 Analyzing Antiderivatives Graphically and Numerically

6.2 Antiderivatives and the Indefinite Integral

Finding Formulas for Antiderivatives

Antiderivatives of Periodic Functions

6.3 Using The Fundamental Theorem to Find Definite Integrals

6.4 Application: Consumer and Producer Surplus

6.5 Application: Present and Future Value

Present and Future Values of an Income Stream

6.6 Integration by Substitution

Using Substitution with Periodic Functions

Definite Integrals by Substitution

PROJECTS: Quabbin Reservoir, Distribution of Resources, Yield from an Apple Orchard

If the derivative of *F*(*x*) is *f*(*x*), that is, if *F*′(*x*) = *f*(*x*), then we call *F*(*x*) an *antiderivative* of *f* (*x*). For example, the derivative of *x*^{2} is 2*x*, so we say that

In this section, we see how values of an antiderivative, *F*, are computed using the Fundamental Theorem of Calculus when the derivative, ...

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