Area Function for a Piecewise Curve

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Adjust the values for and to see the area between the piecewise curve and the -axis over the interval [, ]. Check the box to see the graph of the area as a function of , and observe the effect of changing the value of .

Contributed by: Charles E. Oelsner (Manlius Pebble Hill School) (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

This demonstrates that for a fixed value of , the area between a curve and the -axis over [, ] is a function of . It is then natural to consider the derivative of this area function, which motivates one part of the fundamental theorem of calculus. Note that the area function is smooth, while its derivative, the piecewise-defined curve, is not.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send