Integrate X²e^-x²: Solving a Tricky Integral

[arsmath]

I am working on an integral I am finding tricky, and I think I'm missing something.
I need to integrate on the interval 0 to infinity, x²e^-x².
We have proved that on the interval of -∞ to ∞, e^-x²=√∏ so from o to ∞, it equals √∏/2. I can use this in my proof, but I don't see how. When I try integrating by parts I have trouble getting a finite answer. I would love some help,

 

[Rainbow Child]

Try integrating by parts the

$$I=\int_0^\infty e^{-x^2}\,d\,x$$

 

[sutupidmath]

Try integrating by parts the

$$I=\int_0^\infty e^{-x^2}\,d\,x$$

HOw can one integrate this by parts, i do not think this has any closed form does it?

 

[sutupidmath]

and this question is already on another forum!lol

 

[Rainbow Child]

HOw can one integrate this by parts, i do not think this has any closed form does it?

Like this:

$$I=\int_0^\infty e^{-x^2}\,d\,x=\int_0^\infty (x)'\,e^{-x^2}\,d\,x$$

and

$$I=\frac{\sqrt{\pi}}{2}$$

by OP

 

[sutupidmath]

Like this:

$$I=\int_0^\infty e^{-x^2}\,d\,x=\int_0^\infty (x)'\,e^{-x^2}\,d\,x$$

and

$$I=\frac{\sqrt{\pi}}{2}$$

by OP

At what level is one supposed to learn how to integrate this?? I mean where is it covered?
Becasue this is my first time seeing such a trick!

 

[Rainbow Child]

Did you read the original post?
They gave him the result $I=\frac{\sqrt{\pi}}{2}$.

As for the actual calculation, there are many ways to calulate $I$. The simplest one is by double integrals.

 

[arsmath]

my fault

and this question is already on another forum!lol

i posted in the other forum before finding this one which I think may be more appropriate.

 

[sutupidmath]

Did you read the original post?
They gave him the result $I=\frac{\sqrt{\pi}}{2}$.

As for the actual calculation, there are many ways to calulate $I$. The simplest one is by double integrals.

Well, i did not read the op's post!
and as for evaluating that integral, i think i should wait a few more months.

 

[sutupidmath]

i posted in the other forum before finding this one which I think may be more appropriate.

ok then, like Hurky said, show what u did so far?

 

[arsmath]

At what level is one supposed to learn how to integrate this?? I mean where is it covered?
Becasue this is my first time seeing such a trick!

I'm studying improper integrals for a "topics in advanced math" course. . .the proof is lengthy and involves double integrals and polar coords

 

[sutupidmath]

I'm studying improper integrals for a "topics in advanced math" course. . .the proof is lengthy and involves double integrals and polar coords

AH, i have never worked with double integrals, so i guess i cannot be of any further help, but surely the other guys will give u enough hints to get it right!
good luck!