The ratio of the areas of two regions of the curve C1 : 4x2 + π2y2 = 4π2 divided by the curve C_{2} : y = - sgn \left(\right. x - \frac{\pi}{2} \left.\right) cosx , \textrm{ }\textrm{ } is (Note: where sgn x denotes signum function of x.)

Engineering

Mathematics

Introduction to Area

Question

The ratio of the areas of two regions of the curve C₁ : 4x² + π²y² = 4π² divided by the curve
$C_{2} : y = - sgn (x - \frac{π}{2}) cosx, is$

(Note: where sgn x denotes signum function of x.)

$\frac{π^{2} - 2}{π^{2} + 2}$

$\frac{π^{2} + 4}{π^{2} - 2 \sqrt{2}}$

$\frac{π^{2} + 6}{π^{2} + 3 \sqrt{2}}$

$\frac{π^{2} + 1}{π^{2} - \sqrt{2}}$

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$C_{2} : y = {\begin{cases} - cosx, x > π / 2 \\ cosx, x < π / 2 \end{cases}$

Areas A₁ and A₂ are equal

$∴ reguried ratio = \frac{π^{2} - 2}{π^{2} + 2}$