Find Equal Area Between y=x^2 and y=9

[mikesown]

Homework Statement

"Find a horizontal line y=k that divides the area between y=x^2 and y=9 into two parts"

Homework Equations

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.

 

[christianjb]

Find the two areas as a function of k.

 

[mikesown]

Find the two areas as a function of k.

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

 

[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)

 

[Hurkyl]

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.

 

[HallsofIvy]

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?