Chapter 6 NotesThe Definite Integral1Area1.1What is Area?
Aregionis a set of points in a plane and apolygonalregion isa polygon, together with its interior.We can always find the area of a polygon by cutting it up into triangles andfinding the sum of the areas of the individual triangles.
LetRbe a region in the plane. We say thatRis bounded if thereis a polygonal region that entirely containsR.
LetRbe a region in the plane. IfPis a polygonal region thatcontainsR, we sayPis acircumscribedpolygon forR. IfPis a polygonalregion that lies entirely inside the regionR, we callPaninscribed polygonofR.
We call the greatest lower bound of areas of circumscribed poly-gons ofRtheouter areaofR.1