(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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)

2. Relevant equations

Improper integrals, integration by parts

3. 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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# Homework Help: Decay formula with Improper Integrals

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