My Math Forum Calculate mass along thread (line-integral)

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 October 31st, 2017, 08:31 AM #1 Member   Joined: Oct 2016 From: Sverige Posts: 32 Thanks: 2 Calculate mass along thread (line-integral) I've tried to solve this 4 times already, what am I doing wrong?
 October 31st, 2017, 08:41 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,120 Thanks: 1101 You're doing it wrong :P There's no force here to dot with $dr$ You just have to calculate the differential length along the string and multiply it by the density. I.e. $m = \displaystyle \int_0^1 ~(1+t)\left\|\dfrac{dr}{dt}\right \|~dt$ see if you can chug through the integral. Thanks from topsquark
 October 31st, 2017, 10:44 AM #3 Member   Joined: Oct 2016 From: Sverige Posts: 32 Thanks: 2 integral of (1+t)sqrt(9 + 36t + 36t^2) ? **** me this is the second exercise in this subject, doing mega complex integrals is not part of the course. Is there a simpler way?
October 31st, 2017, 11:03 AM   #4
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 Originally Posted by Addez123 integral of (1+t)sqrt(9 + 36t + 36t^2) ? **** me this is the second exercise in this subject, doing mega complex integrals is not part of the course. Is there a simpler way?
$\left\| \dfrac{dr}{dt} \right \| = \sqrt{9+36t^2 + 36t^4} = 3+6t^2,~t \in [0,1]$

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