How I came to know about this badass method??
(Article by Pranesh Pyara Shrestha)
So, what the heck is this "DUIS Method" ??
Here, the DUIS stands for Differentiation Under the Integral Sign. This is, in my mind, one of the coolest and the most satisfying way of integrating. Like just imagine how cool and badass is it integrate a function with the partial derivatives embedded in it, sounds cool, doesn't it??
Surely you're joking!!! might be your reaction when I say you can differentiate under the integral sign....
Here, I am not going to do any maths, I am just going to present how I came to know this "supercool" technique! Many of the readers may know that I am a huge admirer of Nobel Prize laureate, Richard P. Feynman. I have read many of his masterpieces like "Six easy pieces", "Surely you're joking Mr. Feynman", "Pleasure of finding things out", and many more, the list goes on and on..... Mine personal favourite is Surely you're joking Mr. Feynman. This book is the one, where I first got introduced to this badass method of integral calculus.
In his autobiography "Surely you’re joking, Mr. Feynman", Richard Feynman discusses his “different box of tools”. Among other things, he mentions a tool he picked up from the text Advanced Calculus by Woods, of differentiating under the integral sign – “it’s a certain operation... that’s not taught very much in the universities”.
And I hereby quote word to word from this thrilling book - It seems some things haven’t changed in the way calculus is taught, since I was never exposed to this trick in classes either. However, I’ve accidentally stumbled upon several elegant applications of the maneuver, and thought I’d write a couple of them down.
Then he mentions some of the mathematics(which I previously mentioned, I won't do here) of the differentiating under the integral sign. If the reader wants to know more details about this amazing method and the man himself, you can check the following links which I have provided below:
Brilliant's article on DUIS trick
Wiki's article on Richard Feynman
Video on the simple use of Feynman Technique(by blackpenredpen)
And lastly, if anyone interested, you may legally buy the copy of the Feynman's masterpiece via Amazon
If anyone interested in pdf(illegal way), you can download it here: