27
$\begingroup$

I don't know how to evaluate it. I know there is one method using the gamma function. BUT I want to know the solution using a calculus method like polar coordinates.

$$\int_{-\infty}^\infty x^2 e^{-x^2}\mathrm dx$$

I will wait for a solution. Thank you.

  • 30
    Every day I see someone here asking how to "solve" an integral. One does not "solve" integrals. One solves equations; one solves problems. One _evaluates_ integrals.2011-09-20
  • 3
    I would say **calculate** or **evaluated** -- a *problem* is (if we are lucky) solved, an *expression* might sometimes be calculated.2011-09-20
  • 1
    [Here](http://math.stackexchange.com/questions/26925) is a more general question.2011-09-22
  • 0
    Yes, you don't _solve_ definite_ integrals, you evaluate them.2013-10-18
  • 1
    The question "How do I find $\int_{-\infty}^\infty e^{-x^2}\,dx$" has been asked and answered on this forum many times. I'm surprised so many people bothered to take the time to type a solution as part of the answer to your question when it has been done before. You can convert your integral to that one using integration by parts, with $dv = xe^{-x^2}dx$ and $u = x$. Also, J.M.'s link answers your question.2013-10-18

5 Answers 5