Question

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

x times e to the negative x squared

Answer 1

+∞
∫ 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