(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

evaluate [itex]\int[/itex]e^([itex]\frac{\kappa*x^2}{2KT}[/itex])dx with limits of integration from -infinity to +infinity using the standard form [itex]\int[/itex]e^(-C*x^{2})dx = ([itex]\frac{\pi}{4C}[/itex])^{1/2}with limits of integration from 0 to +infinity. Note κ, k, and T are constants. In the standard form c indicates a constant. Note the function being integrated is an even function: f(x)=f(-x).

3. The attempt at a solution

Well looking at the equation I see C=[itex]\frac{-\kappa}{2KT}[/itex]. I then plug C into ([itex]\frac{\pi}{4C}[/itex])^{1/2}giving ([itex]\frac{-2KT\pi}{4\kappa}[/itex])^{1/2}.

My next step would be to evaluate:

2*[([itex]\frac{-2KT\pi}{4\kappa}[/itex])^{1/2}][itex]^{+infinity}_{0}[/itex]

But I no longer have my variable x to do so, am I missing something? Is my answer simply ([itex]\frac{-2KT\pi}{4\kappa}[/itex])^{1/2}?

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# Evaluate the integral from standard from

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