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Trying to work out the closed curve circulation of a velocity profile. The final integral that has been formed is: $$\int_0^{2\pi}r^3g(t)dt$$

Can somebody help? Not sure whether g(t) can even be integrated?

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    $\begingroup$ There is no picture and you should use Latex for formatting your mathematical notation. $\endgroup$
    – TRF
    Commented Jan 6, 2017 at 22:49
  • $\begingroup$ this is impossible to answer without knowing g. $\endgroup$
    – agentp
    Commented Jan 7, 2017 at 2:26

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Use g(t) as its equivalent (derivative of velocity) and integrate using an abstract function unless the question is assuming g(t) is the constant function used on earth. I think using F = Mmg/r^2 = mdv\dt and substituting g(t) into your function would be a plausible option as g(t) =~a(t). If it's a periodic function then you have the square root relation of T but I'd need more info to confirm. As you are integrating over 2pi I believe g is the relation of a periodic function (root relation), which can be explicitly solved for and plugged into the formula. A picture would certainly clarify! :)

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  • $\begingroup$ how did you get any of that from his simple question? $\endgroup$
    – agentp
    Commented Jan 7, 2017 at 13:47
  • $\begingroup$ Deduction and Newtonian physics? $\endgroup$ Commented Jan 7, 2017 at 20:19

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