# Absolute value integration.

#### integral

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
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 $$\displaystyle |2x| = 2x$$.

#### integral

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

#### Prove It

MHF Helper
So the indefinite would be the integral of positive 2x OR the integral of -2x?
No, it's $$\displaystyle +2x$$ only.