Area of the region x , y : x 2 + y - 2 2 ≤ 4 , x 2 ≥ 2 y is

Step-by-step solution

Given, x 2 + y - 2 2 ≤ 4   &   x 2 ≥ 2 y Now on solving, x 2 + y - 2 2 = 4   &   x 2 = 2 y we get intersecting point of the curves as ± 2 , 2 , Now plotting the diagram we get, So, from above diagram area of required region will be, = 2 1 4 π × 2 2 - ∫ 0 2 2 · y d y = 2 π − 2 ⋅ y 3 2 3 2 0 2 = 2 π - 2 2 3 · 2 2 = 2 π - 8 3 = 2 π - 16 3