What is the integration of |x|?

Solution:

Integration is one of the most important concepts which has diverse applications in many fields of engineering and science.

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

Hence, The integral of |x| is 1/2 x|x|.

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What is the integration of |x|?

Summary:

The integral of |x| is 1/2 x|x|.