Evaluate the following integral: `int_1^3|x^2-2x|dx`

Explanation

Let `I=int_{1}^{3}|x^{2}-2 x| d x`

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| {x}^ (2)-2 {x} = {-(x^{2}-2 x) & `when ` 1 le x lt 2 `

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x^{2}-2 x) ` when `2 le x le 3`

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I=int_{1}^{2}|x^{2}-2 x| d x+int_{2}^{3}|x^{2}-2 x| d x`

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I=int_{1}^{2}-(x^{2}-2 x) d x+int_{2}^{3}(x^{2}-2 x) d x`

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I=-[frac{x^{3}}{3}-x^{2}]_{1}^{2}+[frac{x^{3}}{3}-x^{2}]_{2}^{3}`

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I=-(-frac{4}{3}+frac{2}{3})+(frac{4}{3})`

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I=frac{6}{3}=2`

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