The area (in sq. units) of the region x , y : 0 ≤ y ≤ x 2 + 1 , 0 ≤ y ≤ x + 1 , 1 2 ≤ x ≤ 2 is

Step-by-step solution

0 ≤ y ≤ x 2 + 1 ,   0 ≤ y ≤ x + 1 ,   1 2 ≤ x ≤ 2 Drawing the graph according to the given information, Area is, A = ∫ 1 2 1 x 2 + 1 d x + ∫ 1 2 x + 1 d x A = x 3 3 + x 1 2 1 + x 2 2 + x 1 2 A = 1 3 + 1 - 1 2 3 · 1 3 + 1 2 + 4 2 + 2 - 1 2 + 1 A = 4 3 - 1 24 + 1 2 + 2 + 2 - 3 2 A = 4 3 - 13 24 + 4 - 3 2 A = 32 - 13 + 96 - 36 24 A = 79 24 sq. units.