anonymous
  • anonymous
how do you integrate t times e to the negative t? (te^-t)?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
by parts
anonymous
  • anonymous
(te^-t) just and one to 1then put te over -t+1 te^-t+1/-t+1
anonymous
  • anonymous
\[t e ^{-1/}/-1 +\int\limits e^t dt\]

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amistre64
  • amistre64
very carefully; you dont wana scare it
anonymous
  • anonymous
\[-t/e^t+ e^t +C\]
amistre64
  • amistre64
parts is good ..... e^-t +t -e^-t -1 e^-t +0 ............. right?
amistre64
  • amistre64
-t e^-t + e^-t + C ??
anonymous
  • anonymous
so u=t? and dv=e^-t?
anonymous
  • anonymous
oh missed it :)
amistre64
  • amistre64
yes
anonymous
  • anonymous
so is v=-e^-t?
anonymous
  • anonymous
\[\int\limits_{}^{}te^{-t}dt=-te^{-t}+\int\limits_{}^{}e^{-t}dt=-te^{-t}-e^{-t}+C\]
anonymous
  • anonymous
u=t, du=1 dv=e^-t, v=-e^-t
amistre64
  • amistre64
Lets see if this reverts back... Dt(-t e^-t + e^-t + C) t e^-t - e^-t e^-t (t-1) ... not quite, unless i forgot how to do that too ;)
anonymous
  • anonymous
thanks i got it :)
amistre64
  • amistre64
yay!!

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