5. Applicationsof DefiniteIntegrals...............................................................................................
In this chapter, we will exploresomeof the manyapplicationsof the definiteintegralby usingit to calculate
areasbetweentwo curves,volumes,lengthof curves,and severalotherapplicationsfrom real life suchas
calculatingthe work doneby a force,the pressurea liquidexertson an object,and basicstatisticalconcepts.
AreaBetweenTwo Curves
LearningObjectives
A studentwill be able to:
- Computethe area betweentwo curveswith respectto the - and -axes.
In the last chapter, we introducedthe definiteintegralto find the areabetweena curveand the - axis
over an interval In this lesson,we will showhow to calculatethe area betweentwo curves.
Considerthe regionboundedby the graphs and between and as shownin the figures
below. If the two graphslie abovethe -axis,we can interpretthe area that is sandwichedbetweenthem
as the area underthe graphof subtractedfrom the area underthe graph
Figure1a