Question

The area of the region consisting of points (x, y) satisfying |x ± y | ≤ 2 and x² + y² ≥ 2 is 

(A) 8 - 2π sq. units 

(B) 4 - 2π sq. units 

(C) 1 - 2π sq. units 

(D) 2π sq. units

Answer 1

Answer is (A) 8 - 2π sq. units

see fig.

Shaded region is the required one. Therefore, required area is

4 x 1/2 x 2 x 2 - π . 2 = 8 - 2π sq. units