Finding area with integration and arbitrary line

[zeion]

Homework Statement

Sketch the region bounded by y = x^2 and y = 4. This region is divided into two sub regions of equal area by a line y = c. Find c.

Homework Equations

The Attempt at a Solution

I try to integrate from 0 to a point c and make it equate to from integrating c to 4 like this:

$$<br /> \int_{0}^{c} [(\sqrt{y})-(-\sqrt{y})]dy = \int_{c}^{4} [(\sqrt{y})-(-\sqrt{y})]dy<br />$$

But after I simplify the c disappears.. is this wrong?

 

[Mark44]

Because of the symmetry of this problem, it suffices to look at the region in the first quadrant only.

$$\int_{0}^{c} \sqrt{y}~dy = \int_{c}^{4} \sqrt{y}~dy$$
Try working with this equation - c doesn't disappear.