Find b such that the line y = b divides the region bounded by the graphs of the equations into two regions of equal area.

Given ,

first let us find the total area of the bounded by the curves.

so we shall proceed as follows

as given ,

=>

=>

=>

so

the the area of the region is =

=

=

=

So now we have  to find the horizonal line that splits the region into two regions with area 18

as when the line y=b intersects the curve then the ared bounded is 18,so

let us solve this as follows

first we shall find the intersecting points

as ,

so the area bound by these curves and is as follows

A=

=>

=>

=>

=>

=>

=>

=>

=

but we know half the Area of the region between curves =

so now ,

let

=>

=>

=>

=>

= =

so