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Math Help - Finding a function through its derivatives integration over a finite distance

  1. #1
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    Finding a function through its derivatives integration over a finite distance

    I dont know if this Counts as a differential equation, but here it is. \int_0^d \frac{\partial E}{\partial x}dx=E_0. The condition is that \frac{\partial E}{\partial x}>0 in the interval [0,d] and that E(0)=0 and E(d)=E_0. I can see that a solution is E=xE_0 /d but I dont know how to find this without guessing. Is there a simple method to employ?
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    Re: Finding a function through its derivatives integration over a finite distance

    Quote Originally Posted by fysikbengt View Post
    I can see that a solution is E=xE_0 /d.
    I'm sorry to hear that because it is completely wrong. You seem to be assuming that E is the constant, E_0, which is certainly not true. I'm not sure why you write partial derivatives when you only have the one variable, x. One part of the "Fundamental Theorem of Calculus" say that \int_0^d\frac{dE}{dx}dx= E(d)- E(0). Since we are told that E(0)= E_0 and E(0)= 0, that is E_0- 0= E_0.
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    Lightbulb Re: Finding a function through its derivatives integration over a finite distance

    Quote Originally Posted by HallsofIvy View Post
    I'm sorry to hear that because it is completely wrong. You seem to be assuming that E is the constant, E_0, which is certainly not true. I'm not sure why you write partial derivatives when you only have the one variable, x. One part of the "Fundamental Theorem of Calculus" say that \int_0^d\frac{dE}{dx}dx= E(d)- E(0). Since we are told that E(0)= E_0 and E(0)= 0, that is E_0- 0= E_0.
    Yes, I used an equality by definition so it had to go in circles. But you were good help anyway since I now had to make a more general approach to my original problem doing a variable substitution from x to E to solve it. It was a much shorter and neater proof.
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