6.1 Integral Applications
Area Between Two Functions
Question #4 (Medium): Interpreting the Area Bound by Two Functions
From the integral expression, two functions need to be identified. Graph each function to see which one
lies at the top and bottom. Equate the functions equal to each other to determine the points of
intersection. Usually the interval from the integral matches the points of intersection. Look for or
to see if the functions were integrated over or .
Interpret the integral as the area of a bound region. Then evaluate the integral.
Include the sketch of the region.
∫ ( )
Graphing the component inside the integral is as follows:
Setting the functions equal to each other: ; cross multiply, then
( ) ; moving everything over to on