## anonymous 5 years ago Find the limit of the improper integral

1. anonymous

$\int\limits_{0}^{\infty}(x-1)e^ (-x)$

2. anonymous

Find antiderivative first

3. 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)

4. 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

5. anonymous

then sub in limits , you get zero im fairly sure