Evaluate the definite integral ∫ₐ^b (|x|)/(x) dx, where a<b.
b-a
|b|-|a|
a+b
|a|+|b|
Correct answer: |b|-|a|
Solution
The integral ( rac{|x|}{x}) evaluates to 1 for positive values of x and -1 for negative values of x, leading to the result of (|b| - |a|) when integrating over the interval from a to b, accounting for the sign changes.