Area between functions
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Part of video series
Meets NCTM Standards:
Lesson Description:
Be able to relate the area between two curves (functions) on a Cartesian graph to the algebraic representation as a definite integral of a difference of those two functions. Be able to compute the definite integral of the area between curves given the two functions represented by the curves and limits. Be able to interpret what the area between curves represent with given business functions (e.g. cost and revenue) and compute the area between curves representing a desired business value (e.g. total net profit).
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Additional Resources:
- Computing Technology for Math Excellence - Devoted to the standards movement and integrating technology into teaching and learning and in K-12 mathematics and calculus. Find software and sites for teaching and learning math with technology. Accessibility resources are included.
- Area between curves problem set - A problem set with graphs drawn in for area between curves
Questions answered by this video:
- How do you find the area between curves / functions?
- If you subtract a country's import function from the country's export function and integrate the difference, how do you find the total trade balance for the company for a span of years?
- What is trade balance, trade deficit, or trade surplus?
- How do you find the area between two curves if they overlap and cross paths?
- How can you tell whether an integral will be positive or negative?
- How do you find the area between curves or functions on a TI graphing calculator?
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Staff Review
This lesson explains how to find the area between two functions and how to interpret that area. This area is found for the value of imports for different countries, so the integral has a real-world basis. Trade balance is found for the countries, and the result is explained. This is a great explanation of what finding an integral is really about. A TI graphing calculator is brought in and used at the end of this lesson.
