Need integrating e^(−x^2) x^2

robbbiehu 2022-10-23 Answered
Integrating e x 2 x 2
Show that L { t 1 / 2 } = π / ( 2 s 3 / 2 ) , s > 0
By the definition of Laplace transform we get:
L { t 1 / 2 } = 0 t 1 / 2 e s t d t = { x = s t } = 2 s 3 / 2 0 e x 2 x 2 d x .
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Answers (2)

scranna0o
Answered 2022-10-24 Author has 16 answers
Rewrite the integral as
0 x 2 ( 2 x e x 2 ) d x
and use integration by parts with f ( x ) = x 2 and g ( x ) = e x 2 to obtain
x 2 e x 2 | 0 + 1 2 0 e x 2 d x = π 4
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Cyrus Travis
Answered 2022-10-25 Author has 2 answers
0 x 2 e x 2 d x = 0 x 2 e x 2 ( 2 x d x ) = 0 u 2 e u d u = 1 2 Γ ( 3 2 ) .
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