- #1
matematikuvol
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[tex]\Gamma(x)=\int^{\infty}_0t^{x-1}e^{-t}dt[/tex]
[tex]\Gamma(\frac{1}{2})=\int^{\infty}_0\frac{e^{-t}}{\sqrt{t}}dt=[/tex]
take [tex]t=x^2[/tex]
[tex]dt=2xdx[/tex]
[tex]x=\sqrt{t}[/tex]
[tex]=\int^{\infty}_0\frac{e^{-x^2}}{x}2xdx[/tex]
Why here we can here reducing integrand by [tex]x[/tex]?
[tex]\Gamma(\frac{1}{2})=\int^{\infty}_0\frac{e^{-t}}{\sqrt{t}}dt=[/tex]
take [tex]t=x^2[/tex]
[tex]dt=2xdx[/tex]
[tex]x=\sqrt{t}[/tex]
[tex]=\int^{\infty}_0\frac{e^{-x^2}}{x}2xdx[/tex]
Why here we can here reducing integrand by [tex]x[/tex]?