The area of the region inside the ellipse x 2 + 4 y 2 = 4 and outside the region bounded by the curves y = | x | - 1 a n d y = 1 - | x | is [2026]

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Solution

Q.
The area of the region inside the ellipse $x^{2} + 4 y^{2} = 4$ and outside the region bounded by the curves $y = | x | - 1 and y = 1 - | x |$ is [2026]

1 $3 (π - 1)$

2 $2 (π - 1)$

3 $2 π - 1$

4 $2 π - \frac{1}{2}$

Ans.
(2)

$Required area = area of ellipse - shaded area$

$= π \times 2 \times 1 - 4 (\frac{1}{2} \times 1 \times 1) = 2 π - 2$

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