Q116 / 160 · TS EAMCET 2022 (20 Jul Shift 2) · Mathematics

$\int_0^4|| x-2|-x| d x=$

  • A
    2
  • B
    3
  • Correct answer
    C
    6
  • D
    12

Solution

Given $\int_0^4|| x-2|-x| d x$ Let $I=\int_0^4|| x-2|-x| d x$ $\begin{aligned} & \Rightarrow \mathrm{I}=\int_0^2|2-2 \mathrm{x}| \mathrm{dx}+\int_2^4 2 \mathrm{dx} \\ & =2 \int_0^1(1-\mathrm{x}) \mathrm{dx}+2 \int_1^2(\mathrm{x}-1) \mathrm{dx}+2[4-2] \\ & =1+1+4=6 \end{aligned}$

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

Relevant Questions