# Integral from 0 to Infinity

Not what you're looking for? Search our solutions OR ask your own Custom question.

Show that the

integral from 0 to infinity of (t^n e^-t dt) = n!

Â© BrainMass Inc. brainmass.com December 24, 2021, 5:01 pm ad1c9bdddfhttps://brainmass.com/math/integrals/integral-infinity-22445

#### Solution Preview

By parts,

I = integral(0 to inf)[t^n e^-t dt]

= {-t^n e^(-t)}(U=inf, L=0) + n*integration(0 to inf)[t^(n-1) e^(-t) dt]

Here, U = upper limit = ...

#### Solution Summary

This is how to show a given integral is a factorial.

$2.49