Equal area question

1. Apr 1, 2007

mikesown

1. The problem statement, all variables and given/known data
"Find a horizontal line y=k that divides the area between y=x^2 and y=9 into two parts"

2. Relevant equations

3. The attempt at a solution
Found intersection at (-3,9), (3,9)
Found total area to be 36, half(the area needed for each portion) to be 18. Don't know where to go from here.

2. Apr 1, 2007

christianjb

Find the two areas as a function of k.

3. Apr 1, 2007

mikesown

Can you elaborate more on that? I'm not quite sure what you mean.

4. Apr 1, 2007

christianjb

y=k divides the total area into two parts, A1=A1(k) and A2=A2(k). You need to find an expression for each area as a function of k and then find the value of k for which A1(k)=A2(k)

5. Apr 1, 2007

Hurkyl

Staff Emeritus
Don't be intimidated by the variable k -- the fact it's there changes nothing. You know how to compute areas, so compute the area of one of the portions.

6. Apr 2, 2007

HallsofIvy

Staff Emeritus
What is the area of the region bounded by y= k, y= 9 and y= x2? For what value of k is that 18?

Even simpler: What is the area of the region bounded by y= 0, y= k and y= x2? For what value of k is that 18?