^1_ -1 |1-x|dx is equal to: 1. -2 2. 2 3. 0 4. 4 - Vidyadip

Question

$\int\limits^1_{-1}|1-\text{x}|\text{dx}$ is equal to:

-2
2
0
4

✓

Answer

$2$

Solution:
$\int\limits^1_{-1}|1-\text{x}|\text{dx}$
$=\int\limits^0_{-1}(1-\text{x})\text{dx}+\int\limits^1_0(1-\text{x})\text{dx}$
$=\Big[\text{x}-\frac{\text{x}^2}{2}\Big]^0_{-1}+\Big[\text{x}-\frac{\text{x}^2}{2}\Big]^1_0$
$=0+1+\frac{1}{2}+1-\frac{1}{2}-0$
$=2$

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