Absolute value integration.

Dec 2009
200
35
Arkansas
Such as:

\(\displaystyle \int^{2}_{0} \left | 2x \right |dx\)

How do you solve this?
Thank you in advance


\(\displaystyle \int\)
 

Prove It

MHF Helper
Aug 2008
12,883
4,999
Such as:

\(\displaystyle \int^{2}_{0} \left | 2x \right |dx\)

How do you solve this?
Thank you in advance


\(\displaystyle \int\)
Remember that

\(\displaystyle |X| = \begin{cases}\phantom{-}X\textrm{ if }X \geq 0\\-X\textrm{ if }X < 0\end{cases}\).

So if \(\displaystyle X = 2x\)

\(\displaystyle |2x| = \begin{cases}\phantom{-}2x\textrm{ if }X \geq 0\\-2x\textrm{ if }X < 0\end{cases}\).


In your case, since \(\displaystyle 0 \leq 2x \leq 2\), that means \(\displaystyle |2x| = 2x\).
 
Dec 2009
200
35
Arkansas
So the indefinite would be the integral of positive 2x OR the integral of -2x?