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Integrating V(x)DV(X)

  1. Feb 28, 2010 #1
    I'm in an electronics course, and the book derives an equation for the current-voltage characteristics of an NMOS transistor. In doing so, it integrate this:
    [tex]
    \int_{0}^{V_{DS}}V(X)\, dV(X)=\frac{V_{DS}^2}{2}[/tex]


    I can see that integrating a function F(X) with respect to F(X) turns out to be the same as integrating a single variable such as x with respect to x, but is that mathematically kosher? Can someone convince me that it is?
     
  2. jcsd
  3. Feb 28, 2010 #2

    LCKurtz

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    To see that the antiderivative is

    [tex]\int V(x)dV(x) = \frac{V^2(x)} 2+ C[/tex]

    Just note that

    [tex] \int V(x)dV(x) = \int V(x)V'(x)dx[/tex]

    and that integrand is exactly what you get if you differentiate

    [tex]\frac{V^2(x)} 2+ C[/tex]
     
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