Answer to Question #225934 in Chemical Engineering for Lokika

Question

∫0^∞e^x³ dx is equal to

A) 1/3Γ(1/3)

B) 1/2Γ(1/3)

C) Γ(1/3)           D) 3Γ(1/3)

Answer 1

$$\int_{0}^{\infty}e^{-x^3}dx=\frac{1}{3}\int_{0}^{\infty}e^{-y}y^{1/3-1}dy=\frac{1}{3}\Gamma\left(\frac{1}{3}\right)$$

Answer: A