Asking Laplace to help us solve the Fresnel integral without complex analysis

Here's a really cool approach to solving the Fresnel integral without complex analysis. The technique involves Laplace transforms which provides an elegant solution to this classic integration problem. Oh and here's the link to the integral from zero to infinity of x²/(x⁴+1)
• You're gonna love this...
For the solution using complex analysis, check out:
• These complex gaussian...

[@PrakashPant-h9z]

I really liked your idea of always linking the results from other videos. Quite a good strategy!!!

[@johnannand5449]

Great videos, man. Just found your channel and I can tell you have fun making these which is awesome to see. Have a great day 😊

[@maths_505]

Thanks mate And yes I do have lots of fun solving stuff like this

[@renesperb]

A very interesting application of Laplace transforms , which I so far only used for linear systems of ODE 's . Hidden in the transform of √t is of course the Gauss integral , which you also need if you apply complex anaysis to calculate the Fresnel integral.

[@marcomarino3388]

Nicely solved, well done!!! . Greetings from Italy

[@AJ-et3vf]

Awesome video! Thank you!

[@_P_a_o_l_o_]

I really love your channel! To be honest I prefer when your videos don’t rely on other integrals (such as using values of the Gamma function, or using tables for the Laplace transform). I always wonder if these values/transforms might actually depend on the integral that is being computed in the video, making the calculations circular. This is simply my two cents, please keep up the good work!

[@maths_505]

All that matters is the structure of the integral we're calculating. If that's suitable for an integral transform, we may apply it and that makes the mathematics extremely simple. And to be honest I really love the gamma function and its hard to do higher mathematics without it.

[@Sufiarsh4108]

I m not able to solve maths so fast as u what should I do?

[@TI5040]

Nice 👍👍

[@FreemonSandlewould]

I am sure you have been asked before but: What software tool do you use? Is it a scribe and platter hardware ?

[@maths_505]

I just made a community post about this😂

[@PrakashPant-h9z]

haha. Its hard to be famous!!! @@maths_505