Evaluate: ^3_1|2x-1|dx - Vidyadip

Question

Evaluate:
$\int\limits^3_1|2\text{x}-1|\text{dx}$

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Answer

$\int\limits^3_1|2\text{x}-1|\text{dx}$
$\Rightarrow\int\limits_1^3|2\text{x}-1|\text{dx}=\int\limits^3_1(2\text{x}-1)\text{dx}$
$\Rightarrow\int\limits^3_12\text{x}\text{ dx}-\int\limits^3_1\text{dx}$
$\Rightarrow\Big[\frac{2\cdot\text{x}^2}{2}\Big]^3_1-\big[\text{x}\big]^3_1$
$\Rightarrow[(3)^2-(1)^2]-[(3-1)]$
$\Rightarrow9-1-2=6$

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