Hi Forum!

I have found this question:

Find the horizontal line y=k that divides the area bounded by the curves$\displaystyle y=x^2$and$\displaystyle y=9$in two equal parts.

What I thought:

Get the bounded area.

$\displaystyle \int_{-3}^{3} 9-x^2$

... $\displaystyle =36$

Divide it by two $\displaystyle =18$

and calculate that with line k equaling 18

$\displaystyle \int_{-3}^{3} 9-x^2-k=18$

$\displaystyle 36-3k-3k=18$

$\displaystyle k=3$

But, if we calculate

$\displaystyle \int_{-3}^{3} 3-x^2=0$

This is because we are going to subtract the same area more than once, right?

The answer is probably something around 3 and 6 then.

I am not sure how to continue.

Thanks!