The area of the region, inside the ellipse x²+4 y²=4 and outside the region bounded by the curves y=|x|-1 and y=1-|x| , is :

Step-by-step solution

Ellipse: x^2 4 + y^2 = 1 with a = 2 , b = 1 . Area = ab = 2 . Curves y = |x| - 1 and y = 1 - |x| intersect at x = 1 , forming a rhombus with vertices (0, 1) , (1, 0) , (0, -1) , (-1, 0) . Vertices (0, 1) lie on ellipse; ( 1, 0) are inside ellipse. Area of rhombus = 1 2 2 2 = 2 . Required area = 2 - 2 = 2( - 1) .