The value of int_{a}^{b} frac{x}{|x|} dx,wher | vedclass

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Question

(B) Given the integral $\int_{a}^{b} \frac{x}{|x|} dx$ with the condition $a < b < 0$.Since $x < 0$ for all $x$ in the interval $[a, b]$,we have $|x|

Vedclass · Accepted Answer

$|b| - |a|$

Vedclass · Answer

(B) Given the integral $\int_{a}^{b} \frac{x}{|x|} dx$ with the condition $a Since $x Therefore,the integrand becomes $\frac{x}{|x|} = \frac{x}{-x} = -1$.Now,evaluating the definite integral:$\int_{a}^{b} (-1) dx = -[x]_{a}^{b} = -(b - a) = a - b$.Since $a Thus,$a - b = (-|a|) - (-|b|) = |b| - |a|$.Hence,the correct option is $B$.

The value of $\int_{a}^{b} \frac{x}{|x|} dx$,where $a < b < 0$,is

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