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Math Help - need help with definite integral

  1. #1
    Junior Member
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    need help with definite integral

    find the value of integral(-e to -e^2) (3/x) dx
    (a) -3
    (b)-e
    (c)e^3
    (d)1/3
    (3) none
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  2. #2
    Super Member

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    Hello, Gracy!

    This is a trick question ... on a number of levels.


    Find the value of: . \int^{\text{-}e^2}_{\text{-}e}\frac{3}{x}\,dx

    (a)\;-3\qquad(b)\;-e\qquad(c)\;e^3\qquad(d)\;\frac{1}{3}\qquad(e) \text{ none of these}

    We have: . 3\int^{\text{-}e^2}_{\text{-}e}\frac{dx}{x}\;\,=\;\,3\ln\left|x\right|\,\bigg|  ^{\text{-}e^2}_{\text{-}e}\,\;=\,\;3\ln|\text{-}e^2| - 3\ln|\text{-}e|

    . . . . . = \;\;3\ln(e^2) - 3\ln(e)\;\;= \;\;3(2) - 3(1) \;\;=\;\;\boxed{3}


    Answer: . (e)\text{ none of these}

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