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anonymous

  • 5 years ago

Find the limit of the improper integral

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  1. anonymous
    • 5 years ago
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    \[\int\limits_{0}^{\infty}(x-1)e^ (-x)\]

  2. anonymous
    • 5 years ago
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    Find antiderivative first

  3. anonymous
    • 5 years ago
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    = xe^(-x) -e^(-x) now, apply integration by parts to the first part let u= x dv = e^(-x) dx du= dx v= -e^(-x) integral of first expression is uv - integral ( v du ) = -xe^(-x) + integral e^(-x) dx = -xe^(-x) -e^(-x)

  4. anonymous
    • 5 years ago
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    that takes care of the first expression, but remember we still have to integrate the second expression. integral of the second expression is e^(-x) so sum them up

  5. anonymous
    • 5 years ago
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    then sub in limits , you get zero im fairly sure

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