Linked Questions

2
votes
5answers
337 views

The integral $\int_0^\infty e^{-t^2}dt$ [duplicate]

Me and my highschool teacher have argued about the limit for quite a long time. We have easily reached the conclusion that integral from $0$ to $x$ of $e^{-t^2}dt$ has a limit somewhere between $0$ ...
2
votes
3answers
10k views

Integral from minus infinity to plus infinity [duplicate]

I have come across this formula through one of the members of this forum but i dont know how to prove this formula,can someone help me proving this formula. $\int\limits_{-\infty}^{\infty}e^{-x^2}\...
1
vote
3answers
2k views

$\int e^{-x^2}dx$ [duplicate]

Possible Duplicate: Proving $\int_{0}^{\infty} e^{-x^2} dx = \frac{\sqrt \pi}{2}$ How does one integrate $\int e^{-x^2}\,dx$? I read somewhere to use polar coordinates. How is this done? What ...
2
votes
2answers
3k views

Integral from $0$ to Infinity of $e^{-3x^2}$? [duplicate]

How do you calculate the integral from $0$ to Infinity of $e^{-3x^2}$? I am supposed to use a double integral. Can someone please explain? Thanks in advance.
0
votes
2answers
976 views

How to compute the integral $\int_{-\infty}^\infty e^{-x^2}\,dx$? [duplicate]

How to compute the integral $\int_{-\infty}^\infty e^{-x^2}\,dx$ using polar coordinates?
3
votes
3answers
260 views

Simplest way to integrate this expression : $\int_{-\infty}^{+\infty} e^{-x^2/2} dx$ [duplicate]

I'm toying around with statistics and calculus for a project of mine and I'm trying to find the simplest/fastest way to integrate this formula : $$\int_{-\infty}^{+\infty} e^{-x^2/2} dx$$ I do not ...
2
votes
3answers
616 views

Evaluating $\int_{-\infty}^{\infty}e^{-x^2}dx$ using polar coordinates. [duplicate]

I need to express the following improper integral as a double integral of $x$ and $y$ and then, using polar coordinates, evaluate it. $$I=\int_{-\infty}^{\infty}e^{-x^2}dx$$ Plotting it, we find a ...
2
votes
1answer
474 views

Showing that $\int_{-\infty}^{\infty} \exp(-x^2) \,\mathrm{d}x = \sqrt{\pi}$ [duplicate]

Possible Duplicate: Proving $\\int_{0}^{+\\infty} e^{-x^2} dx = \\frac{\\sqrt \\pi}{2}$ The primitive of $f(x) = \exp(-x^2)$ has no analytical expression, even so, it is possible to evaluate $\...
3
votes
2answers
176 views

How can I evaluate $\int_{-\infty}^{\infty} e^{-x^2} dx$ without using polar coordinates [duplicate]

I know from probability class that the area under the bell curve $e^{-x^2}$ is $\sqrt{\pi}$. I would like to be able to verify this, so in other words, solve this integral: $$\int_{-\infty}^{\infty} e^...
1
vote
2answers
472 views

Integrals involving exponential functions and the gamma function [duplicate]

I'm having trouble evaluating this integral $$\int_0^\infty {e^{-ax^2}} \,dx $$ My guess is that it would evaluate into something like $$\int_0^\infty \frac 12e^{-s}s^{\frac 12} \ldots \,dx = \frac ...
3
votes
2answers
261 views

How do I evaluate the following integral $\int_{-\infty}^{\infty} e^{-\sigma^2 x^2/2}\; \mathrm dx$? [duplicate]

How do I evaluate the following integral $$\int_{-\infty}^{\infty} \exp\left(-\frac{\sigma^2 x^2}{2}\right) \mathrm dx\;?$$ How is it even possible to find an antiderivative? The integral is ...
1
vote
1answer
582 views

Computing the integral of $e^{-x^2}$ over the entire line [duplicate]

Possible Duplicate: Proving $\\int_{0}^{+\\infty} e^{-x^2} dx = \\frac{\\sqrt \\pi}{2}$ At lunch with a math friend years ago, he showed me an integral whose solution was, he said, so beautiful ...
1
vote
1answer
103 views

On evaluating $\int_0^\infty e^{-x^2}\,dx$ [duplicate]

Are there any other methods to integrate the following integral than the ones cited on the Wikipedia page? Maybe with a more elementary tool set? $$\int_0^\infty e^{-x^2}\,dx$$ Addendum: I am not ...
0
votes
3answers
77 views

Integral $\int_{0}^{\infty} e^{-4x^2}dx$ [duplicate]

I'm trying to solve this $$\int_{0}^{\infty} e^{-4x^2}dx$$ I saw how $\int_{\infty}^{\infty} e^{-x^2}dx$ it's done and how it covers the whole plane, then I assume that from $0 \ to \ \infty$ it's ...
1
vote
2answers
86 views

Integrating $\int_{-\infty}^{\infty} e^{-2b x^2} \, dx$ [duplicate]

I need help in integrating this integral: $$\int_{-\infty}^{\infty} e^{-2b x^2} \, dx$$ Knowing the value of $\int_{-\infty}^{\infty} e^{-x^2} \, dx$, and the integral for $e^{bx}$, I'm guessing ...

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