Q234 / 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 $a \lt 0 \lt b$ ?

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

Solution

$\begin{aligned} & l=\int_a^b \frac{|x|}{x} d x \\ & a \lt 0 \lt b\end{aligned}$ $\int_a^b \frac{|x|}{x} d x=\int_a^0 \frac{|x|}{x} d x+\int_0^b \frac{|x|}{x} d x$ $=\int_a^0 \frac{-x}{x} d x+\int_0^b \frac{x}{x} d x=a+b$

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

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