Q96 / 180 · COMEDK 2013 · Mathematics

$\int_{-1}^{1}|1-x| d x$ is equal to

  • A
    $-2$
  • B
    $0$
  • Correct answer
    C
    $2$
  • D
    $4$

Solution

Let $I=\int_{-1}^{1}|1-x| d x$ $$ \begin{aligned} &=\int_{-1}^{1}(1-x) d x \quad\left[\because|x|=\left\{\begin{array}{cc} -x, & x < 0 \\ x, & x \geq 0 \end{array}\right]\right. \\ &=\left[x-\frac{x^{2}}{2}\right]_{-1}^{1}=\left(1-\frac{1}{2}\right)-\left(-1-\frac{1}{2}\right)=\frac{1}{2}+\frac{3}{2}=2 \end{aligned} $$

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

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