Find the ratio of the areas of two regions of the curve `C_(1) -= 4x^(2) + pi^(2)y^(2) = 4pi^(2)` divided by the curve `C_(2) -= y = -(sgn(x - (pi)/(2)))cos x` (where sgn (x) = signum (x)).

Explanation

To find the ratio of the areas of the two regions defined by the curves \( C_1 \) and \( C_2 \), we will follow these steps:

### Step 1: Identify the curves
The first curve is given by the equation:
\[ C_1: 4x^2 + \pi^2 y^2 = 4\pi^2 \]
This can be rewritten as:
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