Alternative solution to the video solution presented by Michael Penn on his YouTube channel today https://t.co/tjhCZYFiUp. I use the beta/gamma functions and identity, Euler’s reflection formula, and Feynman’s trick.
@martinmrmar This book is a classic for differential and integral calculus. As well an excellent book for historical reasons as for the excellent exposition of math. I am also read this book.
30 Days of Feynman—Day 18
Solutions involving differentiating under the integral sign.
An integral formula 2-fer. The solution process includes a simple second order differential equation, and requires knowledge of the Dirichlet integral.
Often done via contour integration.
30 Days of Feynman—Day 5
2 quick ones today.
As a reminder, for 30 days, I plan to publish integral solutions using the Feynman trick. Please feel free to reply with other solution methods, or perhaps more efficient ways of writing solutions using the Feynman trick.
Remember that the derivative of cosh(x)=sinh(x).
For the Laplace transform I used, see 17 in the attached table.
For a cool 😎 result, let b=pi, and a=e.
This is an integral @drpkmath originally posted here, and on his YouTube channel, with a different solution method.
Using the Feynman trick, I introduce a parameter on the first line of the solution, and then differentiate under the integral sign with respect to that parameter.
Another YouTube channel that I’m recommending is Owls Math. He solved the following problem using the King property and trig identities. My trig-free solution involves an interesting property of definite integrals, as illustrated in my reply.