Definite Integration Question 85

Question: The value of $ \int _{a}^{b}{\frac{x}{|x|}dx,a<b<0} $ is

[Orissa JEE 2003]

Options:

A) $ -(|a|+|b|) $

B) $ |b|-|a| $

C) $ |a|-|b| $

D) $ |a|+|b| $

Show Answer

Answer:

Correct Answer: B

Solution:

$ \int_a^{b}{\frac{x}{|x|}dx=-}\int_a^{b}{dx} $ , ( $ \because a<b<0 $ ) $ =-(b-a)=|b|-|a| $ .