CoCalc Public Files2017-02-09-112949.sagewsOpen with one click!
Author: [email protected] Gage
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Description: embedded webwork problem
Compute Environment: Ubuntu 18.04 (Deprecated)

Play with the Geogebra applet above to get a feeling for the relationship between ff, the height
of the upper boundary of the region at xx, and FF, the area of the region to the left of xx.

The example above is simple once you draw the picture! We'll see how this can be reduced to integrating f(x)g(x)f(x)-g(x). To make this visually obvious imagine that the region is composed of vertical tooth picks and then slide them so their butts all rest on the xx-axis. The tooth picks haven't changed length or thickness so the area hasn't changed either. (look up Cavalieri and his principle !)