Let [ t ] denote the greatest integer ≤ t . Then the value of 8 · ∫ - 1 2 1 ( [ 2 x ] + | x | ) d x is

Step-by-step solution

Let I = ∫ - 1 2 1 ( [ 2 x ] + | x | ) d x 2 x will be discontinuous at x   =   0 ,   1 2   ;   x   ∈   - 1 2 ,   1 We know that x   =   x ,   x   ≥   0   ;   - x   ,   x   < 0 . = ∫ - 1 2 0 ( - 1 - x ) d x + ∫ 0 1 / 2 ( 0 + x ) d x + ∫ 1 2 1 ( 1 + x ) d x We know that ∫ x n d x   =   x n + 1 n + 1   +   c = - x - x 2 2 - 1 2 0 + x 2 2 0 1 / 2 + x + x 2 2 1 2 1 =