Domain and Evaluation of Double Integral with Integration by Parts

[2RIP]

Homework Statement

How can i find the integral of \int e^{-x^{3}}dx

Homework Equations

The Attempt at a Solution

I tried using integration by parts, but it doesn't seem to give a nice way to solve either.

 

[rock.freak667]

I do not believe this integral exists in terms of elementary functions. Is it part of a question? If so, post the question.

 

[2RIP]

Sketch the domain of integration of the integral \int^{1}_{0}dy\int^{1}_{\sqrt{y}} e^{-x^{3}}dx and then evaluate it.

 

[Dick]

Sketch the domain of integration of the integral \int^{1}_{0}dy\int^{1}_{\sqrt{y}} e^{-x^{3}}dx and then evaluate it.

Are you answering you own question? If so, that's nonsense.