Question

`int_-1^1(|x|)/(x)` dx, x ≠ 0 is equal to ______.

Options

• −1

• 0

• 1

• 2

Answer 1

`int_-1^1(|x|)/(x)` dx, x ≠ 0 is equal to 0.

Explanation:

`int_-1^1(|x|)/(x)  dx = int_-1^0(|x|)/(x)  dx + int_0^1(|x|)/(x)  dx`

= `int_-1^0 (-x)/(x)  dx + int_0^1(x)/(x)  dx`

= `int_-1^0 -1  dx + int_0^1 1  dx`

= `[-x]_-1^0 + [x]_0^1`

= −[0 − (−1)] + [1 − 0]

= −1 + 1

= 0