Q214 / 270 · NDA 2022 (Phase 1) · Mathematics

What is $\int_{-2}^{-1} \frac{x}{|x|} d x$ equal to?

  • A
    -2
  • Correct answer
    B
    -1
  • C
    1
  • D
    2

Solution

$\begin{aligned} & \int_{-2}^{-1} \frac{\mathrm{x}}{|\mathrm{x}|} \mathrm{dx} \\ & =\int_{-2}^{-1} \frac{\mathrm{x}}{-\mathrm{x}} \mathrm{dx} \\ & =-\int_{-2}^{-1} \mathrm{dx}=-[\mathrm{x}]_{-2}^{-1} \\ & =-\{(-1)-(-2)\}=-1\end{aligned}$

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

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