Feynman's Technique of Integration

Feynman's Technique of Integration is one the most popular techique that we use to solve some hard integration beacause by using normal method doesn't lead us to the answer, so today i'm going to show you a little trick about Feynman's Technique of Integration and I hope it's very useful for you guy to solve integration.

First of all not all integration can be use by this technique and sometime it can be use but you don't it in the right also usless. So how do we know that we are using it right or wrong , well basically we can't that until we try it and the more you do it the more you know how to use it right. So the first that we need to do is trying make a new variable inside the integration sign and then try to diffrentiate it over the integration sign to cancel some part of the integrand or to make it fit with another tichnique like integration by part. NOTE in here when you diffrentiate over the integration sign we call it Leibniz integral rule. So let get into the real example , suppose that I want to solve below integration.

 

so now first step is try to make new function that has a new variable in the integrand, let try:

now diffrentiate over the integration sign that respect to t:

Our goal is after the diffrentiation we hope that it become easier to solve or it can be solve by another way, like now after the diffrentiation we can see that the integration can be solve by the integraton by part , so now let do the integration by part:

As we can see after do the integration by part it turn out to be our function I(t) and we knew that I(1) is the value that we want to know so after solve the diffrential equation we can place t=1 and we will get the answer.

now the integration has been solve , thank you for reading I hope that this article will help you something and comment below about any topic that you guy want me to write about.And finally forget to up vote for more content like this if you like.  ;)