anonymous
  • anonymous
f(x)=x^2*e^(-|x|) how can i solve the integral?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
i now there are some representations of e^x that cant be integrated.... forget why..
amistre64
  • amistre64
but for this; just int by parts using x^2 as u; and v as e^...
anonymous
  • anonymous
Yes, but how i deal the absolute value?

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amistre64
  • amistre64
an absolute value is always positive; and the opposite of an always positive value is always negative right?
amistre64
  • amistre64
just redefine it; |x| = a perhaps
anonymous
  • anonymous
Shouldn't i divide the integral into two cases? |x| = x if x>0 and |x| = -x if x<0?
amistre64
  • amistre64
http://www.analyzemath.com/calculus/Differentiation/absolute_value.html
shadowfiend
  • shadowfiend
Yeah, I think that's the way you have to go.
watchmath
  • watchmath
Is this a definite integral or indefinite?
anonymous
  • anonymous
The exercise is to solve the integral from -inf to inf
watchmath
  • watchmath
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.
amistre64
  • amistre64
thats what I had in mind :) just couldnt spell it out well enough ...

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