 
Hello students, today I'm here with a new topic
'Green theorem'
Before this, it is very important to understand 'line integral'
The previous videos were about line integral and its applications
So please go through the video of 'line integral'
because the main purpose of using green theorem is
to solve the problems of 'line integral' with surface integral or double integral easily
So let me tell you how to do it.
 
 
 
 
 
 
 
 
 
The proofs of the theorems will be in a separate video
but for now, I'm teaching you how to solve problems based on it
 
 
 
The same question, I taught you to solve using line integral in the line integral video
You can go and see it by clicking on the i-icon above
Now I'll teach you how to do it using 'Green theorem'
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Let me tell you that I have already uploaded a video on the area of double integral
 
 
 
 
 
 
So, students, there can be three types of questions based on the green theorem
First, solving this question using line integral that I taught you in that video
Second, solving this question using green theorem that I taught you in this video
Third, verifying this question for the green theorem
When asked to verify, we will first solve it using line integral
then we will solve it using green theorem
and then by comparing both the answers, we will show that they are same
this is how we verify the green theorem
Such questions are asked based on the green theorem
I'll take one or two more questions based on this
So students, let us see one question here
 
 
 
 
 
 
Here you have to verify green theorem which means
firstly we will solve it using line integral
then using green theorem
and then show that both the answers are the same
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
In line integral, there should be only one variable, either x or y
so from here, we can convert it entirely into 'x' or 'y'
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Students, here we are using double integration
if you have any problem regarding it,
you can simply check out the video by clicking on the i-icon
 
So there is a concept in double integration that
we consider the first limit as constant whereas second one as variable
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
So, students, the answer using line integral was 3/2
and using green theorem also we got 3/2
and hence green theorem is verified
Please do understand the concept of line integral beforehand
so that you won't have to face any problem here
I'll take one last question and then we'll end this topic
Hello students, let us move on to the last question
 
 
 
 
 
I have already taught you to solve this question using line integral
and you can see that video by clicking on the i-icon above
There you'll have to understand what is line integral but let me give you a hint
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
So here, the answer by the line integral is 0
and by green theorem is also 0
and you'll have to see the line integral solution in that video
I won't repeat it twice as I have already explained
So students, today I taught you how to verify and apply the green theorem
Its  ain application is to find surface or double integral very easily
But for understanding the concepts of line and double integral, you'll have to go through my previous videos
Thank you so much for watching my video. Keep commenting, keep sharing and keep liking
 
