elmart3aliAyakittne
elmart3aliAyakittne elmart3aliAyakittne
  • 08-08-2016
  • Mathematics
contestada

Another e integration: xe^(-x^2)

x times e to the negative x squared

Respuesta :

HomertheGenius
HomertheGenius HomertheGenius
  • 12-08-2016
+∞
  ∫  x · e ^(-x² ) dx =   /  The substitution:  u = - x²,  x d x = - du / 2  
-∞
                                                              +∞
= - 1/2 ·  ∫ e ^(u)  du  = - 1/2 · e ^(-x²)  /
                                                             - ∞
e^(-∞) = 1 / e^(∞)

= -1/2 · [ 1/ e^(∞) - 1/ e^(∞) ]  = -1/2 · ( 0 - 0 ) = 0
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