The area (in sq. units) of the region A = ( x , y ) : ( x - 1 ) [ x ] ≤ y ≤ 2 x , 0 ≤ x ≤ 2 , where [ t ] denotes the greatest integer function, is :

Step-by-step solution

y = [ x ] ( x - 1 ) = 0 0 ≤ x < 1 x - 1 1 ≤ x < 2 Area = ∫ 0 2 2 x · d x - 1 2 ( 1 ) ( 1 ) = 4 x 3 / 2 3 0 2 - 1 2 = 8 2 3 - 1 2