Evaluate the following integrals: `int_0^2|x^2-3x+2|dx`

Explanation

`int_{0}^{2}|x^{2}-3 x+2| d x`

We know that, `|x^{2}-3 x+2|=`begin array}{l}-(x^{2}-3 x+2) (x^{2}-3 x+2). `
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therefore I=int_{0}^{2}(x^{2}-3 x+2) d x`
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Rightarrow I=int_{0}^{1}(x^{2}-3 x+2) d x-int_{1}^{2}(x^{2}-3 x+2) d x`
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Rightarrow I=[frac{x^{3}}{3}-frac{3 x^{2}}{2}+2 x]_{0}^{1}-[frac{x^{3}}{3}-frac{3 x^{2}}{2}+2 x]_{1}^{2}`
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Rightarrow I=frac{1}{3}-frac{3}{2}+2-[frac{8}{3}-6+4-frac{1}{3}+frac{3}{2}-2] `
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Rightarrow I=frac{1}{3}-frac{3}{2}+2-frac{8}{3}+6-2+frac{1}{3}-frac{3}{2}`
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Rightarrow I=1`
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