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Integrating challenge I am having

  1. Oct 1, 2014 #1
    Hi, I am doing an exercise practice samples for the upcoming quiz, and stumbled across two questions I'm having trouble solving....

    First question is to integrate integral e-x2 dx ...where the solution is equal to pi1/2

    Also...

    As for the second question (of a different equation) how can one solve for the result when I integrated an equation (another example) and got a x*e-x2 = ?, where x = -infinite to x = infinite? The answer is 0, but I don't know how to get there.

    If anyone could explain, I'd appreciate it!
     
  2. jcsd
  3. Oct 1, 2014 #2

    Simon Bridge

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    In the first problem:$$\int e^{-x^2}\;dx$$... where the solution is ##\sqrt{\pi}## ?
    Did you miss out the limits of the integration?
    Over the entire number line, this is called "the Gaussian Integral".
    See: http://en.wikipedia.org/wiki/Gaussian_integral

    For the other one: $$\int_{-\infty}^\infty xe^{-x^2}\; dx = 0 $$ ...you should be able to tell that is true by looking at the symmetry, but you may prefer to use a substitution.
    What have you tried?
     
  4. Oct 1, 2014 #3
    Hello, thank you for hints--I just realized I made a mistake in my substitution. I got 0--and yes, since the area under the one curve is + and the other -, altogether, they become 0.
     
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