Question

explain why this is improper integral:
from 1 to infinity: integral of x^4 e(^-x^4))dx

Answer 1

the infinity

Answer 2

since it has an inifity it shows its improper?

Answer 3

take the limit as x goes to infinity:
you get x^4 going to infinity, but e^-infinity is going to zero:

so your limit looks like this:

lim = infinity*0

we have no idead whether the limit will converge or not, so we can't actually take an integral of it going to infinity

Answer 4

yes...that is one way to be in improper integral