Area under the curveHard
Question
The area of the region, inside the ellipse $x^{2} + 4y^{2} = 4$ and outside the region bounded by the curves $y = |x| - 1$ and $y = 1 - |x|$, is :
Options
A.$2(\pi - 1)$
B.$2\pi - \frac{1}{2}$
C.$3(\pi - 1)$
D.$2\pi - 1$
Solution
Required area $=$ area of ellipse - shaded area
$$= \pi \times 2 \times 1 - 4\left( \frac{1}{2} \times 1 \times 1 \right) = 2\pi - 2$$
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