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anonymous
 5 years ago
what is the integral of xe^x with limits 0 to infinity?
anonymous
 5 years ago
what is the integral of xe^x with limits 0 to infinity?

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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}

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

anonymous
 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 \[\lim_{b \rightarrow \inf} \frac{1}{e^b}=\lim_{b \rightarrow \inf}e^{b}=0\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ah i see! thank you so much for your help :)
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