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Antiderivatives and Slope Fields

Indefinite integration, or antidifferentiation, is the process of recovering a function from its derivative. In particular, recovering a position function from a velocity function is an important application example. A slope field is a powerful tool that takes advantage of the idea of local linearity to provide a graphical interpretation for antiderivatives. The unit also includes other lessons on the most important symbolic techniques of indefinite integration are the method of substitution and integration by parts.

Calculus: Antiderivatives and Slope Fields Activities

Title Type

Integration By Parts

Students investigate the product rule of differentiation and integration by parts.

Alignments  Standards  |  Textbook  
  • 3761

Integration By Substitution

Students explore methods for computing integrals of functions that are not in one of the standard forms.

Alignments  Standards  |  Textbook  
  • 3466

Slope Fields Introduction

Explore the concept of slope field to the first order differential equation.

Alignments  Standards  |  Textbook  
  • 5714

Slope Fields

Use a visual representation of the family of solutions to a differential equation.

Alignments  Standards  |  Textbook  
  • 5295

Elevator Height as Integral of Velocity

Work with linked representations of the vertical motion of an elevator.

Alignments  Standards  |  Textbook  
  • 4721

Velocity, Position, Distance

Work with linked representations of the horizontal motion of an object.

Alignments  Standards  |  Textbook  
  • 4835
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