6.1 Integral Applications
Area Between Two Functions
Question #1 (Easy): Evaluating the Area Between Two Functions From the Graph
The graph shows the shaded region bound by two functions ( ) and ( ) where ( ) ( )over the
interval[ ]. The area of the shaded region is: ∫ [ ( ) ( ) ] .
To evaluate, the interval has to be defined where the top and bottom function merges into a point.
These are called the points of intersection and there must be at least two. This is determined by setting
the functions equal to each other, and then solving for the unknown variable .
Then which function lies at the top and bottom need to be determined in order to properly set the
expression in the integral over .
Find the area of the shaded region bound by the functions
and √ .
Two functions given are: and √ . From the graph the top and bottom functions
are: √ and . So, ( ) √ and ( ) .
Since the interval is not specified, point o