# Math Help - Gamma Function

1. ## Gamma Function

$\displaystyle\int_0^{\infty}\frac{1}{5}xe^{-\frac{x}{5}} \ dx$

$\displaystyle\Rightarrow\frac{1}{5}\lim_{b\to\inft y}\int_0^b xe^{-\frac{x}{5}} \ dx=5\Gamma(2)=10$

Correct?

2. Originally Posted by dwsmith
$\displaystyle\int_0^{\infty}\frac{1}{5}xe^{-\frac{x}{5}} \ dx$

$\displaystyle\Rightarrow\frac{1}{5}\lim_{b\to\inft y}\int_0^b xe^{-\frac{x}{5}} \ dx=5\Gamma(2)=10$

Correct?
try the substition

$x=5u \implies dx=5du$

$\displaystyle \frac{1}{5}\int_{0}^{\infty}(5u)e^{-u}(5du)=...$
yes It is I made a mistake at first

3. Originally Posted by TheEmptySet
try the substition

$x=5u \implies dx=5du$

$\displaystyle \frac{1}{5}\int_{0}^{\infty}(5u)e^{-u}(5du)=...$
yes It is I made a mistake at first
That is what I did. Is the answer I have correct?

4. No $\Gamma(2)=1$