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Could someone help me in evaluating this integral please? :

$$\int_{0}^x t^2\exp(-t^2) dt$$

By error function method please

I spliced the integrand into $t\cdot t\cdot \exp(-t^2)$ then doing integral by parts I arrived to $-\frac{x}{2}\exp(-x^2)+\frac{1}{2}\text{erf}(x)$

But in my problem set the result is given by $-\frac{x}{2}\exp(-x^2) + \frac{\sqrt{\pi}}{4}\text{erf}(x)$

I don't know what is the problem here Please help

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  • $\begingroup$ There are different definitions of the error function which differ just by their coefficient. That is likely the only difference here. $\endgroup$ – Paul Dec 5 '16 at 20:28
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    $\begingroup$ The usual definition is $\text{erf}(x)=\frac{2}{\sqrt{\pi}}\int_0^x \exp(-t^2)dt$ $\endgroup$ – Frank Lu Dec 5 '16 at 20:29
  • $\begingroup$ Thanks a lot. I missed to multiply and divide by 2/sqrt(pi) $\endgroup$ – Student404Mus Dec 5 '16 at 20:44

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