I have this improper integral:
$$\int_{-\infty}^{\infty}xe^{-x^2}\ dx$$
During my lecture we were told to find whether it converges or diverges, and I found it converged because after calculating the integral:
$$ \frac{-e^{-x^2}}{2}$$
I can see adding infinity for x will make the fraction $=0$. We were told it was a trick question, something something about negatives, and we moved on. But I'm still wondering why the answer isn't that it converges because it still looks correct to me?