Integration Problem

  • Thread starter qspeechc
  • Start date
  • #1
840
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Homework Statement



[tex] \int_{0}^{\infty}x^3.e^{-x^2} \mathrm{d}x [/tex]

The Attempt at a Solution



I have tried substitution u=x^2, u=x^3; integration by parts; squeeze theorem; partial fraction decomp; taylor series expansion- but nothing seems to work. I know the limit of [tex]x^3.e^{-x^2}[/tex] as x tends to infinity is zero, but that doesn't help.
Any help please?
 

Answers and Replies

  • #3
840
14
Well, ok.

Let u = x^2 , then: du = 2x.dx. And then what? We have an x^3 in the integration, so I don't see how it works.
 
  • #4
2,076
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But x3 = x.x2, isn't it?
 
  • #5
840
14
Yes, but then we would have:

[tex]x^2.e^{-u}.du[/tex] or am I missing something?
 
  • #6
2,076
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[tex]x^2.e^{-u}.du[/tex] or am I missing something?
You just did the sub u=x^2 a couple of steps ago.
 
  • #7
840
14
AHA!!! Oh thank-you neutrino! I can't believe I never saw that! Gee, I feel like an idiot! Thank-you again!
 
  • #8
2,076
2
AHA!!! Oh thank-you neutrino! I can't believe I never saw that! Gee, I feel like an idiot! Thank-you again!

You're welcome. Make a hobby out of solving integrals (if you're into those kind of things), and you'll start recognising the methods with just a look at the integral. (For some of them, at least. :biggrin:)
 
  • #9
840
14
Actually I quite dislike calculus. I find it dry and boring. Or atleast that's the way my first year course presents it. But I guess you are right, I need to do more calculus problems if I want to be a mathematician :tongue:, which I do.
 

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