What Is The Integral Of |x|. - Cuemath

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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.

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