I'm having a hard time evaluating this integral.(adsbygoogle = window.adsbygoogle || []).push({});

A Gaussian pulse [tex]\psi (y,t) = Ae^{-( \frac{y-ct}{a} )^2}[/tex] is travelling in an infinite string of linear mass density [tex]\rho[/tex], under tension [tex]T[/tex].

I know the Kinetic Energy is the integral of the partial: [tex]\frac{\rho}{2} \int_{-\infty}^{\infty} (\frac{\partial \psi}{\partial t})^2 dy[/tex]. I evaluate the partial, and this simplifies to [tex]\frac{\rho}{2} \int_{-\infty}^{\infty} (\frac{2c(y-ct)}{a^2} \psi)^2 dy[/tex].

I don't know where to proceed from here. I tried u-substitution, and integration by parts, with no success. I think the error function is useful in this, but we haven't covered this in the physics course yet.

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# Tough wave energy integral

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