Q235 / 270 · NDA 2023 (Phase 1) · Mathematics

Paragraph: Let $l=\int_a^b \frac{|x|}{x} d x, \quad a \lt b$
Question: What is $l$ equal to when $\mathrm{a} \lt \mathrm{b} \lt 0$ ?

  • A
    $a+b$
  • Correct answer
    B
    $a-b$
  • C
    $b-a$
  • D
    $\frac{(a+b)}{2}$

Solution

$a \lt b \lt 0$ $\int_a^b \frac{|x|}{x} d x=\int_a^b \frac{-x}{x} d x=a-b$

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

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