Is [0,∞] e^(-x^3) dx an Improper Integral?

[Jbreezy]

Homework Statement

It just wants me to tell whether this is improper or not.
[0,infinity] e^(-x^3) dx

Homework Equations

I say Yes

The Attempt at a Solution

 

[haruspex]

I don't see why it would be improper. What's your reasoning?

 

[Jbreezy]

I'm not 100 percent sure. I said yes because I think it keeps going it's domain is all real.

 

[Ray Vickson]

Homework Statement

It just wants me to tell whether this is improper or not.
[0,infinity] e^(-x^3) dx

Homework Equations

I say Yes

The Attempt at a Solution

What definition of "improper integral" are you using?

 

[Mark44]

Homework Statement

It just wants me to tell whether this is improper or not.
[0,infinity] e^(-x^3) dx

Homework Equations

I say Yes

The Attempt at a Solution

I would call this integral --
$$\int_0^{\infty}e^{-x^3}dx$$
-- improper, because of the upper limit of integration.

 

[Jbreezy]

I'm just using the def in stewart calc. I think it is improper thanks.