does-the-rule-of-odd-and-even-functions-can-be-applied-with-improper-integration-I-xe-x-2-dx-while-f-x-xe-x-2-is-odd-then-I-0-

Question Number 208842 by NasaSara last updated on 24/Jun/24

d o e s t h e r u l e o f o d d a n d e v e n f u n c t i o n s

c a n b e a p p l i e d w i t h i m p r o p e r i n t e g r a t i o n ?

I = \int_{- \infty}^{\infty} {x e}^{- x^{2}} d x

w h i l e f (x) = {x e}^{- x^{2}} i s o d d

t h e n I = 0

Commented by Frix last updated on 24/Jun/24

Yes .

Answered by mathzup last updated on 24/Jun/24

I = {l i m}_{a \to + \infty} \int_{- a}^{a} {x e}^{- x^{2}} d x = 0

p u i s q u e l a f o n c t i o n x \to {x e}^{- x^{2}} e s t i m p a i r e

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