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Please Solve RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.3 Question 1 Subquestion (iv) Maths Textbook Solution.

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Answer:  1

Hint: Break the range of integration  \left\{\begin{array}{c} -1<x<0 \\ 0<x<2 \end{array}\right\}

Given:   \int_{-1}^{2} \frac{|x|}{x}


                \begin{aligned} &|x|=\left\{\begin{array}{l} -x, \text { if }-1 \leq x \leq 0 \\ x, \text { if } 0 \leq x \leq 2 \end{array}\right\} \\ \end{aligned}

                \frac{|x|}{x}=\left\{\begin{array}{l} -1,-1<x<0 \\ 1,0<x<2 \end{array}\right\} \\

                I=\int_{-1}^{0}(-1) d x+\int_{0}^{2}(1) d x


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