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lelandsthename
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Homework Statement
Hey everyone! I have another question about improper integrals, they're so hard!
M = -k [tex]\int[/tex][tex]\stackrel{inf.}{0}[/tex] te^(kt) dt
When k = -0.000121 (Carbon 14's constant, we are solving for the mean life of a carbon-14 isotope)
Homework Equations
Improper integrals, integration by parts
The Attempt at a Solution
=- k lim[tex]_{t->inf.}[/tex] [tex]\int[/tex]te^(kt) dt from 0 to infinity
by parts:
u = t
du = dt
dv = e^(k) dt
v = (1/k)e^(-kt)
=(t((1/k)e^(kt)) + [tex]\int[/tex](1/k)e^(kt)dt
=((t)/(k))e^(-0.000121t) - (1/((k)^2)e^(kt)
=- k lim[tex]_{t->inf.}[/tex] [tex]\int[/tex](t)/(k)e^(kt) - (1/(k)^2)e^(kt)
Where can I go from here? I can put both terms over (k)^2 but the limit of that term times e^(k) equals 1*, right? So is hte answer just -k? Somehow I am skeptical!
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