Mathematics

$$\int_0^\infty  {{x^n}{e^{ - x}}dx} $$ (n is +ve integer) is equal to


ANSWER

$$n!$$


SOLUTION
$$\displaystyle \int _{ 0 }^{ \propto  }{ { x }^{ n }{ e }^{ -x }dx= } \Gamma \left( n+1 \right)$$ $$=n!$$

$$\because  gamma function$$
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Single Correct Medium Published on 17th 09, 2020
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