# Thread: Integrate the following equation

1. ## Integrate the following equation

Question : Integrate $\displaystyle \int_{-1}^{1} |1- x| dx$

2. Originally Posted by zorro
Question : Integrate $\displaystyle \int_{-1}^{1} |1- x| dx$
Note that $\displaystyle |1 - x| = 1 - x$ when $\displaystyle x < 1$ and |$\displaystyle 1 - x| = -(1 - x) = x - 1$ when $\displaystyle x \geq 1$.

3. or note that the integrand is non-negative for $\displaystyle -1\le x\le1,$ so the absolute value is irrelevant there and you can simply evaluate $\displaystyle \int_{-1}^1(1-x)\,dx.$

4. Originally Posted by zorro
Question : Integrate $\displaystyle \int_{-1}^{1} |1- x| dx$
$\displaystyle \forall x\in [-1,1],1-x\geq 0$

5. ## Is this correct?

Originally Posted by Raoh
$\displaystyle \forall x\in [-1,1],1-x\geq 0$

$\displaystyle \int_{-1}^{1} |1-x|dx \$= $\displaystyle \int_{-1}^{1} (1-x)dx$ = ........ = $\displaystyle 2$

Is this correct???

6. Originally Posted by zorro
$\displaystyle \int_{-1}^{1} |1-x|dx \$= $\displaystyle \int_{-1}^{1} (1-x)dx$ = ........ = $\displaystyle 2$

Is this correct???
i believe you're right