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Integrating V(x)DV(X)

  • Thread starter xcvxcvvc
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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?
 

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  • #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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