If a < b < 0 then ∫ab| x |xdx =

∫ab(x)xdx=∫ab−xxdx (∵ x<0) =(−x)ab =a−b

If a < b < 0 then ∫ab| x |xdx =

∫ab(x)xdx=∫ab−xxdx (∵ x<0) =(−x)ab =a−b

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If a < b < 0 then $\int_{a}^{b} \frac{| x |}{x} d x$ =

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a – b

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Detailed Solution

$\int_{a}^{b} \frac{(x)}{x} d x = \int_{a}^{b} \frac{- x}{x} d x$ $(∵ x < 0)$

$= {(- x)}_{a}^{b}$

$= a - b$

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If a < b < 0 then $\int_{a}^{b} \frac{| x |}{x} d x$ =