What is it about?
The paper demonstrates how changes in elevation of any integral function over a horizontal region always computes the area swept out by its corresponding derivative function from the horizontal axis.
Featured Image
Why is it important?
Recognizing the relationships between integrals and their derivatives helps one understand why changes in the height of any integral always equals the magnitude of square area traced out by its derivative, and thus how the Calculus can be trusted to solve innumerable problems with applications in the natural world.
Perspectives
Many Calculus students, after reading this study, finally grasp well how the area swept out by a derivative along the horizontal axis is exactly equal to the change in elevation of its integral over that domain, and why this fact holds regardless of the curvature or shape of the two smooth functions. Those who learn this have helped others who have completed Calculus courses by explaining how any integral automatically sums the total area of an essentially infinite number of filament areas traced out by its derivative.
Dr. Richard Sauerheber
Palomar Community College
Read the Original
This page is a summary of: Teaching demonstration of the integral calculus, International Journal of Mathematical Education in Science and Technology, May 2019, Taylor & Francis,
DOI: 10.1080/0020739x.2019.1614689.
You can read the full text:
Contributors
The following have contributed to this page
