Q117 / 160 · AP EAMCET 2024 (21 May Shift 2) · Mathematics

$\int_1^5(|x-3|+|1-x|) d x=$

  • A
    4
  • B
    8
  • Correct answer
    C
    12
  • D
    24

Solution

$\begin{aligned} & \text { }|x-3|= \begin{cases}3-x, & x \lt 3 \\ x-3, & x\gt3\end{cases} \\ & \text { and }|1-x|=x-1 ; x\gt1 \\ & I=\int_1^5(|x-3|+|1-x|) d x \\ & =\int_1^3(3-x+x-1) d x+\int_3^5(x-3+x-1) d x \\ & =\int_1^3 2 d x+\int_3^5(2 x-4) d x=4+\left[x^2-4 x\right]_3^5=12 .\end{aligned}$

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

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