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Evaluate the following integral: int1^3|...

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

Text Solution

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Consider `I = int_(1)^(3) |x^(2) -2x| dx`
" " |x^(2) - 2x| = `{{:(-(x^(2)-2x),,when" "1le x lt2),((x^(2)-2x),,when" "2 le x le 3):}`
`I = int_(1)^(2)|x^(2) -2x|dx + int_(2)^(3) |x^(2) - 2x| dx `
`I = int_(1)^(2) -(x^(2) - 2x)dx + int_(2)^(3) (x^(2) - 2x) dx`
`I = - [ (x^(3))/(3) - x^(2)]_(1)^(2) + [(x^(3))/(3) - x^(2)]_(2)^(3)`
`I= -(-(4)/(3) + (2)/(3)) + ((4)/(3))`
`I = (6)/(3) = 2`
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