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anonymous

  • 5 years ago

f(x)=x^2*e^(-|x|) how can i solve the integral?

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  1. amistre64
    • 5 years ago
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    i now there are some representations of e^x that cant be integrated.... forget why..

  2. amistre64
    • 5 years ago
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    but for this; just int by parts using x^2 as u; and v as e^...

  3. anonymous
    • 5 years ago
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    Yes, but how i deal the absolute value?

  4. amistre64
    • 5 years ago
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    an absolute value is always positive; and the opposite of an always positive value is always negative right?

  5. amistre64
    • 5 years ago
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    just redefine it; |x| = a perhaps

  6. anonymous
    • 5 years ago
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    Shouldn't i divide the integral into two cases? |x| = x if x>0 and |x| = -x if x<0?

  7. amistre64
    • 5 years ago
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    http://www.analyzemath.com/calculus/Differentiation/absolute_value.html

  8. shadowfiend
    • 5 years ago
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    Yeah, I think that's the way you have to go.

  9. watchmath
    • 5 years ago
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    Is this a definite integral or indefinite?

  10. anonymous
    • 5 years ago
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    The exercise is to solve the integral from -inf to inf

  11. watchmath
    • 5 years ago
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    That makes a difference \(\int_{-\infty}^\infty x^2e^{-|x|}=2\int_0^\infty x^2e^{-x}\,dx\) and you can use integration by parts.

  12. amistre64
    • 5 years ago
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    thats what I had in mind :) just couldnt spell it out well enough ...

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