# What is the integration of |x|?

Integration is one of the most important concepts which has diverse applications in many fields of engineering and science. Let's solve one such problem.

## Answer: The integral of |x| is 1/2 x|x|.

Let's understand the solution in detail.

**Explanation:**

We have to solve the integral ∫ |x| dx.

We use integration by parts to solve this:

⇒ u = |x|

⇒ du = |x| / x dx

⇒ v = 1

⇒ dv = dx

Now, using the formula of integration by parts:

⇒ ∫ |x| dx = |x| x − ∫|x| dx

Now, we add ∫ |x| dx on both sides:

⇒ 2 ∫ |x| dx = |x| x

⇒ ∫ |x| dx = 1/2 |x| x