Let the area enclosed by the lines x + y = 2 , y = 0 , x = 0 and the curve f ( x ) = min x 2 + 3 4 , 1 + [ x ] where [ x ] denotes the greatest integer ≤ x , be A . Then the value of 12 A is

Step-by-step solution

Given, The lines x + y = 2 ,   y = 0 , x = 0 and the curve f ( x ) = min x 2 + 3 4 , 1 + [ x ] where [ x ] denotes the greatest integer ≤ x , Now plotting the diagram of given function we get, Now from above diagram, the area enclosed is given by, A = ∫ 0 1 2 x 2 + 3 4 d x + 1 2 1 2 + 3 2 × 1 = 5 12 + 1 ⇒   12 A = 17