The value of integral `underset(a)overset(b)int(|x|)/(x)dx`, `a lt b` is :

Options

A. `|b| - |x|`
B. `|a| - |b|`
C. `(|b|)/(|a|)`
D. `0`

Answer

A

Explanation

`int_(a)^(b) (|x|)/(x) dx`
when `x ge 0`
`rArr int_(a)^(b) x/x dx`
`rArr int_(a)^(b) (1) dx`
`= [x]_(a)^(b) = |b| - |a|`
when `x lt0`,aas `0lt a lt b`, x will not lie between a and not b so
`int_(a)^(b) (|x|)/(x) dx =0` for `x lt 0`