anonymous
  • anonymous
Find the limit of the improper integral
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\int\limits_{0}^{\infty}(x-1)e^ (-x)\]
anonymous
  • anonymous
Find antiderivative first
anonymous
  • anonymous
= 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)

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anonymous
  • anonymous
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
anonymous
  • anonymous
then sub in limits , you get zero im fairly sure

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