# Thread: Integration of e

1. $\int^2_0 e^{x^2} \, dx$ So....How do I integrate this? I thought it would be easier, but I'm stuck.

Thanks

I'm wondering if we're going to have an x in the denominator of the final solution. I tried that, and looked into using l'hopital's rule, but I think I'm getting the integral wrong first.

Thanks.

2. the integral is non-trivial, so you aren't going to get an antiderivative unless, $\frac{1}{2}\sqrt{\pi} Erfi(x)$ means something to you

3. try

$
\int e^{f(x)}dx = \frac{e^{f(x)}}{f'(x)}+c
$

4. No, that does not work in this case

if you are just looking for arbitrary precision, I would find the Taylor series for e^x^2 and integrate term by term

5. There's no clean way to integrate. It's an even function, though. Not that I could tell you how that helps going from 0 to 2.

6. ## Well I got a solution on my graphics calculator

Yeah it is even function.
I got a solution on my calculator for this integral of 16.45....
I'm really only experimenting with the integration to answer another problem.
I will post that one next, it's really a probability question but because I have to integrate a gaussian pdf I might get away with putting it in here.

Maybe my query will make more sense.

7. Find the taylor series for $e^{x^{2}}$
Then integrate and plug in numbers.

8. Originally Posted by Bucephalus
$\int^2_0 e^{x^2} \, dx$ So....How do I integrate this? I thought it would be easier, but I'm stuck.

Thanks

I'm wondering if we're going to have an x in the denominator of the final solution. I tried that, and looked into using l'hopital's rule, but I think I'm getting the integral wrong first.

Thanks.
An exact answer in terms of a finite number of elementary functions does not exist. This can be proved but I don't see the point.

You are no doubt expected to get an approximate answer to a required number of decimal places using teachnology. Perhaps the question where this comes from even says that ....? So that's what you should do.

Originally Posted by Bucephalus
Yeah it is even function.
I got a solution on my calculator for this integral of 16.45....
I'm really only experimenting with the integration to answer another problem.
I will post that one next, it's really a probability question but because I have to integrate a gaussian pdf I might get away with putting it in here.

Maybe my query will make more sense.
Your calculator gives an approximate value, not an exact one.