Q115 / 160 · TS EAMCET 2023 (13 May Shift 2) · Mathematics

If $[\mathrm{x}]$ represents greatest integer function then $\int_{-2}^2[2-x] d x=$

  • A
    10
  • Correct answer
    B
    6
  • C
    4
  • D
    3

Solution

$\begin{aligned} & \text {} \int_{-2}^2[2-x] d x \\ & =\int_{-2}^{-1}[2-x] d x+\int_{-1}^0[2-x] d x+\int_0^1[2-x] d x+\int_1^2[2-x] d x \\ & =\int_{-2}^{-1} 3 d x+\int_{-1}^0 2 d x+\int_0^1 1 d x+\int_1^2 0 d x\end{aligned}$ $\begin{aligned} & =[3 x]_{-2}^{-1}+[2 x]_{-1}^0+[x]_0^1 \\ & =(-3+6)+(0+2)+1=6 .\end{aligned}$

Hence, the correct answer is option: 'B'.

Relevant Questions