A community for students.
Here's the question you clicked on:
 0 viewing
Star
 5 years ago
what is the integral of xe^x with limits 0 to infinity?
Star
 5 years ago
what is the integral of xe^x with limits 0 to infinity?

This Question is Closed

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1\[\int\limits_{}^{}xe^{x}dx=xe^{x}\int\limits_{}^{}e^{x}dx=xe^{x}e^{x}\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1before we look at the limits lets check this

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1(1)e^{x}x(e^{x})+e^{x} =xe^{x} YAY! now for the limists...

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1\[\lim_{b \rightarrow \inf}(be^{b}e^{b}+e^0)\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1e^0=1 e^{b}>0 as b>inf now let's look at be^{b}

star
 5 years ago
Best ResponseYou've already chosen the best response.0we are using limits because it is improper integral?

star
 5 years ago
Best ResponseYou've already chosen the best response.0ahh i see. i was wondering where the e^0 came from?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1i plugged in ther limits the bottom limit is 0 [0e^0e^0]=+e^0=+1

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1\[\lim_{b \rightarrow \inf}be^{b}=\lim_{b \rightarrow \inf} \frac{b}{e^b}=\lim_{b \rightarrow \inf} \frac{1/e^b}\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1\[\lim_{b \rightarrow \inf}be^{b}=\lim_{b \rightarrow \inf} \frac{b}{e^b}\]

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.1use l'hospital's rule so we have \[\lim_{b \rightarrow \inf} \frac{1}{e^b}=\lim_{b \rightarrow \inf}e^{b}=0\]

star
 5 years ago
Best ResponseYou've already chosen the best response.0ah i see! thank you so much for your help :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.