let-the-gamma-function-be-defined-by-gammapint0infty-xp-1e-xdx-evaluate-gammalef

Question

Let the gamma function be defined by Γ(p)=∫0∞x p−1e−x dx\Gamma(p)=\$$int_0$$^{\infty}$$x^{\,p-1}$e^{-x}$$\,dx. Evaluate Γ ⁣(32)\Gamma\!\left(	frac{3}{2}ight) by using the substitution x=u2x=$$u^{2}. ($$Hint: you may use the Gaussian integral identity ∫0∞e−u2 du=π2\$$int_0$$^{\infty}$$e^{-u^2}$$\,du=\frac{\sqrt{\pi}}{2}.)

Accepted Answer

π2\dfrac{\sqrt{\pi}}{2}

Answer

2π2\sqrt{\pi}

Answer

π\pi

Answer

π2\dfrac{\pi}{2}