How to set up and solve an equation to find the vertical line that bisects the region?

Answer: check explanation

Step-by-step explanation:

To find a general method on how to solve an equation to find the vertical line that bisects the region we will have to find the area between the curve. For instance, if we are to find a number A and the line y=A divides the region between the curved of y = X^2, say y = 4.

In the example given above, there is a need to solve for A. We will the take A and zero as the upper and lower limit boundaries respectively. That's ∫| (√4 - ydy) | = 16/3.

Then, 16/3 = 2 ∫ (A - x^2) provided that the upper and lower limit boundaries are √b and 0 respectively. And, this is the case because because the function is even.

Therefore, A = 14/3.

The upper limit on the integral is where the curve meets the line y=A.