Calculus
Area Under Curves, Conic Sections
jee_main_2026_jan_21_shift_1
Grade None
Question:
The area of the region, inside the ellipse x² + 4y² = 4 and outside the region bounded by the curves y = |x| - 1 and y = 1 - |x|, is:
A. 2(π-1)
B. 2π - 1/2
C. 3(π-1)
D. 2π - 1
Step-by-Step Solution
Key Concept: Find area of ellipse and subtract area of the diamond-shaped region.
Step 1: Ellipse: x² + 4y² = 4 => x²/4 + y² = 1. Area = π(2)(1) = 2π. Step 2: y = |x| - 1 and y = 1 - |x| form a square with area = 2. Step 3: Required area = 2π - 2 = 2(π-1).
Correct Answer: A
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