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Math Help - Integration

  1. #1
    Newbie
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    May 2008
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    Post Integration

    Use integration to solve for value from 4 to 2

    xe^(4-x)

    Could someone show me how to do this question I know its by parts but it get lost and end up with an enormous answer, stage by stage would be a great help thank you
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, pip1690!

    \int^4_2 xe^{4-x}\,dx

    . . \begin{array}{ccccccc}u &=& x &\quad & dv &=&e^{4-x}dx \\<br />
du &=& dx & \quad & v &=& -e^{4-x} \end{array}


    We have: . -xe^{4-x} + \int^4_2e^{4-x}dx \;\;=\;\;-xe^{4-x} - e^{4-x}\,\bigg]^4_2 \;\;=\;\;-e^{4-x}(x+1)\,\bigg]^4_2


    . . =\;\;\bigg[-e^0(5)\bigg] - \bigg[-e^2(3)\bigg]\;\;=\;\;-5 + 3e^2

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