What is the integral of |x|.

Solution:

The absolute function has an algebraic expression written within the absolute symbol such that f (x) = | x | which has all non-zero numbers.

Let f (x) or y = |x|

The function absolute value of x can be defined as | x | = { x if x ≥ 0, - x if x < 0.

To find the integral of |x|.

⇒ ∫ |x| dx = { ∫ x if x ≥ 0, ∫ - x if x < 0.

⇒ ∫ x if x ≥ 0 and  ∫ - x if x < 0

⇒  x¹⁺¹ / 1+1  if x ≥ 0  and  - x¹⁺¹ / 1+1 if x < 0

⇒  x² / 2 if x ≥ 0  and  - x² / 2 if x < 0

Thus, the integral of absolute value of x is x² / 2 if x ≥ 0  and - x² / 2 if x < 0.

What is the integral of |x|.

Summary:

The integral of |x| is x² / 2 if x ≥ 0  and - x² / 2 if x < 0.