## Mix Limit Derivative and Integral

Anyone can do it?? then compare with my answer =$-\frac{1}{4}$ 😀 I don’t want to post it 😀 I’m not sure my solution is right or wrong 😀 thank you 😀 My answer that I got is completely wrong 😀

We given ${{f}^{'}}(x)={{e}^{-{{x}^{2}}}}$ and $\underset{x\to +\infty }{\mathop{\lim }}\,f(x)=0$

find the solution of $\int\limits_{0}^{+\infty }{{{x}^{2}}f(x)dx}$ 😀