6.1 Integral Applications
Area Between Two Functions
Question #2 (Medium): Evaluating the Area Between Two Functions Without a Graph
When two functions are given without a graph, then first graphing the function is helpful. Also, one of
the first steps to set aside is determining the points of intersection between two functions by setting
them equal to each other. If the bound area falls within two vertical lines of values, the integral should
be with respect to . If the bound area falls within two horizontal lines of values of points of
intersection, the integral should be over . This is expressed as: ∫ [ ] . The function
setting the right boundary is , and the function setting the left boundary is . The interval is[ ]
where and are the values of the points of intersection.
Sketch the area bound by the given functions. Decide whether to integrate over the variable or .
In the sketch also include an approximating rectangle with the labeled height and width. Then evaluate
the area of the bound region.
The graph of two functio