find the value of ( b ) so that the line y=b divides the region bound by the graph of the tow functions f(x)= 9-x^2 , g(x)=0 into regions of equal area
good, then let $\displaystyle y = b$ be the horizontal line that cuts the region's area in half.
using symmetry, note that the area of the region in quadrant I is $\displaystyle \displaystyle \int_0^3 9 - x^2 \, dx = 18$
since $\displaystyle y = 9-x^2$ , $\displaystyle x = \sqrt{9-y}$ , and ...
$\displaystyle \displaystyle \int_0^b \sqrt{9-y} \, dy = 9$
evaluate the integral and solve for $\displaystyle b$