1. ## integral

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

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
What have you tried to solve this?

3. sorry, i have not idea to solve

sorry, i have not idea to solve
start by calculating the area of the region between $\displaystyle y = 9-x^2$ and the x-axis ... you'll need that piece of information to find the "half" area.

what do you get?

5. the area of the region between f(x)=9-x^2 and the x-axis equal 36

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 $\displaystyle b$