# Math Help - Absolute value integration.

1. ## Absolute value integration.

Such as:

$\int^{2}_{0} \left | 2x \right |dx$

How do you solve this?

$\int$

2. Originally Posted by integral
Such as:

$\int^{2}_{0} \left | 2x \right |dx$

How do you solve this?

$\int$
Remember that

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

So if $X = 2x$

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

In your case, since $0 \leq 2x \leq 2$, that means $|2x| = 2x$.

3. So the indefinite would be the integral of positive 2x OR the integral of -2x?

4. Originally Posted by integral
So the indefinite would be the integral of positive 2x OR the integral of -2x?
No, it's $+2x$ only.