0-e-x-4-dx-1-4-please-prove-it-

Question Number 97465 by hosein_golmakani last updated on 08/Jun/20

\int_{0}^{\propto} e^{- x^{4}} d x = \frac{1}{4}

p l e a s e p r o v e i t

Commented by PRITHWISH SEN 2 last updated on 08/Jun/20

let x^{4} = z

dx = \frac{1}{4} z^{- \frac{3}{4}} dz

\frac{1}{4} \int_{0}^{\infty} e^{- z} z^{(\frac{1}{4} - 1)} dz = \frac{1}{4} Γ (\frac{1}{4})

Answered by smridha last updated on 08/Jun/20

l e t x^{2} = t

s o I = \frac{1}{2} \int_{0}^{\infty} e^{- t^{2}} t^{- \frac{1}{2}} d t

= \frac{1}{4} [2 \int_{0}^{\infty} e^{- t^{2}} t^{2 \frac{1}{4} - 1} d t]

= \frac{1}{4} Γ (\frac{1}{4})

I t h i n k A n s i s w r o n g . .

Answered by mathmax by abdo last updated on 08/Jun/20

error in the question \dots!