$\mathop \smallint \nolimits_a^b \,\,\frac{{\left| {\,x\,} \right|}}{x}\,\,dx,\;\,a < 0 < b$, is equal to

$\left| {\,a\,\, - \,\,b\,} \right|$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \nolimits_a^b \,\,\frac{{\left| {\,x\,} \right|}}{x}\,\,dx,\;\,a < 0 < b

, is equal to

View answer and explanation

Correct option: A

\left| {\,b\,} \right|\,\, - \,\,\left| {\,a\,} \right|

Option A (

\left| {\,b\} \right|\, - \,\left| {\,a\} \right|

) is correct because the integral of |x|/x from a to b, where a < 0 < b, simplifies to b - (-a) = |b| - |a|.

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