anonymous
  • anonymous
Does anyone know how to evaluate the integral of e^f(x) dx
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\int\limits_{?}^{?}e^{f(x)}dx\]
anonymous
  • anonymous
there is no fixed process for determining the integral as there is in differentiating, where the chain rule allows an analytic solution ( a formula) to be determined. Although some functions have analytic solutions, not all do, for example, $$\int e^{x^2}} /; dx $$ I believe does not have an analytic solution, but $$\int xe^{x^2}} /; dx $$ does Hope that helps, - any comments from anyone else please - as I am not sure this is a very clear answer.
anonymous
  • anonymous
Yeah.... true enough... I am trying to get a solution to a differential equation and well its not going to well specifically \[d^{2}v/dx^{2} = -\beta*e^{v}\]

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anonymous
  • anonymous
sorry - at work - so keep getting taken away. just to confirm, that is e^v and beta is as constant.
anonymous
  • anonymous
I agree with John P. There's no way you could solve it without knowing f(x). Even if you knew f(x) most likely there's no closed solution. This might not be satisfying but you could always use numerical integration (Simpson, trapezoidal, etc) to evaluate an integral between a and b.
anonymous
  • anonymous
Well its really a Boundary value problem with these condtions dv/dx=0 at x=0, v(1)=0 and v(0)=Vinitial and the bounds for the diff eq is 0

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