Integrate the following equation

• Dec 14th 2009, 02:43 AM
zorro
Integrate the following equation
Question : Integrate $\displaystyle \int_{-1}^{1} |1- x| dx$
• Dec 14th 2009, 02:47 AM
mr fantastic
Quote:

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 $\displaystyle x \geq 1$.
• Dec 14th 2009, 03:51 AM
Krizalid
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 $\displaystyle \int_{-1}^1(1-x)\,dx.$
• Dec 14th 2009, 04:05 AM
Raoh
Quote:

Originally Posted by zorro
Question : Integrate $\displaystyle \int_{-1}^{1} |1- x| dx$

$\displaystyle \forall x\in [-1,1],1-x\geq 0$
• Dec 14th 2009, 11:18 AM
zorro
Is this correct?
Quote:

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???
• Dec 14th 2009, 11:28 AM
Raoh
Quote:

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(Nod)