6.1 Integral Applications
Area Between Two Functions
Question #6 (Medium): Finding the Missing Variable From the Area Between Two Functions
After establishing the expression for the area bound by two functions ∫ [ ( ) ( ) ] , work
backwards to find any missing variable. Graph the area bound by the functions as a helpful guide which
helps to see which function lies at the top and bottom. Setting the right order of ( ) ( ) is very
important. Then the rest of the calculation is applying various integral properties to simplify and finding
the missing variable.
Find the value of where the region enclosed by the functions and is .
The given functions are written in terms of . Graphing the functions also indicate that the integral
should be done over . Then, ∫ [ ] . Since sets the right boundary,
; and since sets the left boundary, .
-intercept means . So equatin