The value of the integral, ∫ 1 3 x 2 - 2 x - 2 d x , where x denotes the greatest integer less than or…

The value of the integral, ∫13x2-2x-2dx, where x denotes the greatest integer less than or equal to x, is
  1. -4
  2. -5
  3. -2-3+1
  4. -2-3-1

Solution

∫13x-12-3dx

=∫02x2dx-3∫13dx

=∫010dx+∫121·dx+∫232·dx+∫323·dx-6

=2-1+23-2+32-3-6

=-2-3-1

Asked in: JEE Main 2021 (24 Feb Shift 2)

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