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