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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Definite Integration

NDA 2023 · Mathematics · Definite Integration

Paragraph: Let l=∫_a^b (|x|)/(x) d x, a Question: What is l equal...

Paragraph: Let l=∫ab∣x∣xdx,a<bl=\int_a^b \frac{|x|}{x} d x, \quad a < b
Question: What is ll equal to when a<0<ba < 0 < b ?

Options

  1. Aa+ba+b
  2. Ba−ba-b
  3. Cb−ab-a
  4. D(a+b)2\frac{(a+b)}{2}

Correct answer

A. a+ba+b

Step-by-step solution

l=∫ab∣x∣xdxa<0<b\begin{aligned} & l=\int_a^b \frac{|x|}{x} d x \\ & a < 0 < 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$
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