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.
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