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Fundamental theory of calculus

  1. Apr 7, 2012 #1
    1. The problem statement, all variables and given/known data
    The question:

    The function F(θ,k) is defined as

    [tex]F(\theta,k)=\int_0^θ (f(x,k))\mathrm{d}x[/tex]

    Find expressions for [itex]\left({\frac{\partial F}{\partial \theta}}\right)_k[/itex] and [itex]\left({\frac{\partial F}{\partial k}}\right)_θ[/itex]

    2. Relevant equations
    Fundamental theory of calculus
    Chain rule?


    3. The attempt at a solution
    I think [itex]\left({\frac{\partial F}{\partial \theta}}\right)_k[/itex] is just [itex]f(\theta,k)[/itex] - is that correct? or is it [itex]f(\theta,0)[/itex] because [itex]k[/itex] is held constant so when it is differentiated it will be 0.

    I'm a little stumped by the second part. Is there some way to re-express it in terms of [itex]\left({\frac{\partial F}{\partial\theta}}\right)_k[/itex] using the chain rule?
     
  2. jcsd
  3. Apr 7, 2012 #2

    Dick

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