If-I-1-2-0-t-n-e-t-dt-360-Find-n-

Question Number 46465 by rahul 19 last updated on 26/Oct/18

I f I = \frac{1}{2} \int_{0}^{\infty} t^{n} e^{- t} d t = 360 .

F i n d n ?

Answered by tanmay.chaudhury50@gmail.com last updated on 26/Oct/18

g a m m a f u n c t i o n

\int_{0}^{\infty} e^{- t} t^{n - 1} d t = ⌈ (n)

w h e n ⌈ (n + 1) = n ⌈ (n) = n!

y o u r p r o b l e m i s

\frac{1}{2} \int_{0}^{\infty} e^{- t} t^{n + 1 - 1} d t

\frac{1}{2} \times ⌈ (n + 1) = 360

n! = 360 \times 2 = 720 = 6!

s o n = 6

Commented by rahul 19 last updated on 27/Oct/18

thanks sir! ��