Improper Integrals: Integrating Over Infinite Limits

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This informational material will explain how to evaluate integrals with infinite limits to find the value of a variable. It gives examples of integrals with limits of infinity or negative infinity that converge or diverge. There are corresponding videos available. Practice questions with a PDF answer key are provided.  

Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.7

Determine numerically, algebraically, and graphically the limits of functions at specific values and at infinity.

UP:MA19.PRE.7

Vocabulary

  • Limit
  • Convergent
  • Divergent
  • Continuous function
  • Discontinuous function
  • Discontinuity (infinite, jump, removable)

Knowledge

Students know:
  • How to graph the families of functions.
  • How to factor, simplify, and rationalize functions.
  • How to evaluate functions at a given input value.

Skills

Students are able to:
  • Identify continuity and discontinuity (if discontinuous, identify the type).
  • Calculate limits.

Understanding

Students understand that:
  • Functions have various types of continuity and discontinuity.
  • That limits can be determined numerically, graphically, and algebraically.
  • converging means that a limit exists, while diverging means that a limit does not exist.

CR Resource Type

Informational Material

Resource Provider

CK-12

License Type

Custom

Accessibility

Text Resources: Content is organized under headings and subheadings
Video resources: includes closed captioning or subtitles
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