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

$$IfI=\frac{1}{2}{\int }_0^{\mathrm{\infty }}{t}^n{e}^{-t}dt=360.$$$$Findn?$$

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

$$gammafunction$$$${\int }_0^{\mathrm{\infty }}{e}^{-t}{t}^{n-1}dt=\lceil \left(n\right)$$$$when\lceil (n+1)=n\lceil \left(n\right)=n!$$$$$$$$yourproblemis$$$$\frac{1}{2}{\int }_0^{\mathrm{\infty }}{e}^{-t}{t}^{n+1-1}dt$$$$\frac{1}{2}\times \lceil (n+1)=360$$$$n!=360\times 2=720=6!$$$$son=6$$

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

thanks sir! ����

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