## anonymous 5 years ago whats the integral of xe^(4-x) as x approaches infinity?

1. mathteacher1729

$\int_{}^{\infty} xe^{4-x}dx$ What is the lower limit? really can't do much without that.

2. anonymous

oops, sorry! 4

3. mathteacher1729

$\int_{4}^{\infty} xe^{4-x}dx$ is that the problem?

4. anonymous

yes correct

5. anonymous

its not infinity or -infinity, but I cannot find out the answer

6. anonymous

Integrate by parts u=x and dv=e^4-x change infinity to t, then evaluate as a limit

7. anonymous

(as t goes to infinity)

8. anonymous

$\lim_{4 \rightarrow \infty} -x e^{4-x} -e^{4-x} ?$

9. anonymous

? i have no idea...

10. anonymous

x--->infinity

11. anonymous

*

12. anonymous

Yep, you got the integral right. now sub in your upper and lower limits. Now you should have something with t in it ( y(t) ) Take the limit of this as t goes to infinity