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Please solve RD Sharma class 12 chapter 19 Definite Integrals exercise Very short answer type question 9 maths textbook solution

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Answer: -1

Hint: You must know the integration rules of trigonometric function with its limits

Given: \int_{-2}^{1} \frac{|x|}{x} d x

Solution:  \int_{-2}^{1} \frac{|x|}{x} d x

\begin{aligned} &=\int_{-2}^{0} \frac{-x}{x} d x+\int_{0}^{1} \frac{x}{x} d x \\\\ &=\int_{-2}^{0}-1 d x+\int_{0}^{1} 1 d x \end{aligned}

\begin{aligned} &=-[x]_{-2}^{0}+[x]_{0}^{1} \\\\ &=-[0+2]+[1+0] \\\\ &=-2+1 \\\\ &=-1 \end{aligned}

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