JEE Mains · Maths · STD 12 - 8. Application and integration
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:
- A \( 2(\pi-1) \)
- B \( 2\pi-\frac{1}{2} \)
- C \( 3(\pi-1) \)
- D \( 2\pi-1 \)
Answer & Solution
Correct Answer
(A) \( 2(\pi-1) \)
Step-by-step Solution
Detailed explanation
Required area = area of ellipse - shaded area \( =\pi\times2\times1-4(\frac{1}{2}\times1\times1)=2\pi-2 \)
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