9.8.3 Area of the region bounded between two curves

. . Area of the region bounded between two curves Case (i) Let y ( ) and y g x ( ) be the equations of two curves in the XOY − plane such that g x ≥ for all x a b ∈ [ , ] . We want to find the area A of the region bounded between the two curves, the ordinates x and The required area is sketched in Fig. . . To compute A , we divide the region into thin vertical strips of width D x and height g x . It is important note that f x g x ≥ for all a b ∈ [ , ] . As before, the required area is the limit of the sum of the areas of the vertical strips. Hence, we get A = [ ( ) ( )] g x dx O x = x = π x = π Fig. . Fig. . ( , ( )) x f x g x ( , ( )) x g x O of - - Applications of Integration Note Viewing in the positive direction of y − axis, the curve y ( ) can be termed as the upper curve (U) and the curve y g x ( ) as the lower curve (L). Thus, we get A y dx U L