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A green function

  1. Aug 8, 2012 #1
    1. The problem statement, all variables and given/known data

    The problem is attached in the first picture, the provided solutions are in the second.


    3. The attempt at a solution

    I got to where they are, but aren't they missing an additional term of sin(t)*cos(∏)*f(∏) from the second integral in dx/dt ?
     

    Attached Files:

  2. jcsd
  3. Aug 8, 2012 #2
  4. Aug 8, 2012 #3
    Ok! I worked it out finally. Will the leibniz rule work if i take 'cos(t)' and 'sin(t)' out of the integral such that the inside of the integral only becomes one variable: ∫-sin(ζ)f(ζ) and ∫-cos(ζ)f(ζ) ??


    The answer seems to use the leibniz rule but they imply that the 'cos(t)' and 'sin(t)' were taken out of the integral..
     
  5. Aug 8, 2012 #4
    cos(t) and sin(t) are treated as constants in the integral because the integral is with respect to zeta, and the integral itself is treated as a constant in differentiation because the derivative is taken with respect to t. The function inside inside the integral that involves t is differentiated as usual, and the integral is treated as a constant so it is left as-is.
     
  6. Aug 8, 2012 #5
    Sorry I'm not sure what you mean but here's the method that I used (attached in the picture)

    In the picture its ∫ f(x,t) from u to v.

    In the question of this thread, I am above to take 'sin(t)' and 'cos(t)' out of the integration so that the integration only has 1 variable.

    My question is:

    How do we still apply (or can we) leibniz's rule if this is the case? (Only 1 variable)
     

    Attached Files:

  7. Aug 8, 2012 #6
    Yes, you can, just take f(x,t)=f(t) (check the link I gave about differentiation under the integral sign.)
     
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