Absolute value integration.

• May 15th 2010, 07:55 PM
integral
Absolute value integration.
Such as:

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

How do you solve this?
Thank you in advance

$\displaystyle \int$
• May 15th 2010, 08:14 PM
Prove It
Quote:

Originally Posted by integral
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 $\displaystyle |2x| = 2x$.
• May 15th 2010, 10:15 PM
integral
So the indefinite would be the integral of positive 2x OR the integral of -2x?
• May 15th 2010, 10:30 PM
Prove It
Quote:

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

No, it's $\displaystyle +2x$ only.