6.1 Integral Applications
Area Between Two Functions: Overview
For two continuous functions and where for all over the interval [ ], the
area between two functions is given by: ∫ [ ]
This is approximated by: ∑ [ ] ∑ [ ] , where
represents the top function and the bottom function.
Thus, the estimating rectangles have the of [ ] and the of .
1) To evaluate the area bound by two functions where a specified interval is not given, then first
the points of intersection between two functions must be determined in order to establish the
interval. For any two given functions, there must be at least two points of intersection. These
relate to the beginning and the ending points which set the interval to be [ ].
2) Next from two functions, the one that lies at the top and bottom need t