Difference between revisions of "Fresnel S"
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| − | [https://www.youtube.com/watch?v=fFZ6BsH99-0 The Fresnel Integral S(x) - How to integrate sin(x^2)] | + | [https://www.youtube.com/watch?v=fFZ6BsH99-0 The Fresnel Integral S(x) - How to integrate sin(x^2)]<br /> |
<center>{{:*-integral functions footer}}</center> | <center>{{:*-integral functions footer}}</center> | ||
Revision as of 02:34, 4 June 2015
The Fresnel $S$ function is defined by $$S(x)=\int_0^x \sin(t^2) dt.$$
- Fresnel.png
Fresnel integrals on $\mathbb{R}$.
Properties
Theorem: The following limit is known: $$\displaystyle\lim_{x \rightarrow \infty} S(x) = \displaystyle\int_0^{\infty} \sin(t^2)dt = \sqrt{ \dfrac{\pi}{8}}.$$
Proof: █
Videos
The Fresnel Integral S(x) - How to integrate sin(x^2)
