# Homework Help: Finding area with integration and arbitrary line

1. Feb 8, 2010

### zeion

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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:

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

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

2. Feb 8, 2010

### Staff: Mentor

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.