Hello students, today I am here with a new topic and the topic is the application of line integral before this, I have taught line integral to you if you have not watched that video then you can go and press the 'I' tab and go through to my old videos here I have told what is gradient, curl concept of diversion how to find the derivative of direction these all 2-3 old video you can go through and watch that video then understand these this concept then there will be no difficulties in learning so today we will discuss that application of line integral so 1st application is work done 1 note is there that at the place 'F ' it is a velocity then we called them as circulation of 'F' around curve c 2nd application is independent of the path if there is some force and it is not dependent on its path how to find this if it is an irrotational vector or it is a conservative irrotational vector field so directly we can do its independent path if we solve this and directly we will use its limit and we do its integration so I will explain to you with a question without that you will not get that let's see the question what is the concept of the scalar potential let's take an example if a take a gradient of this scalar students if you don't know what is a gradient then you can go then click on 'I' tab and go through my old video their I have explained about what is a gradient here I will not able to explain the concept of gradient if I take its curl then its curl will be 0 gradient curl is 0 now what is the scalar potential this is a scalar and we have taken its gradient then it became a vector this type of vector is given now the question may be asked that this vector is of which scalar, means whose gradient we have taken and it became a vector we have to find F this F is called a scalar potential this f is made of a function of a gradient this need to be understand simply I will explain to you that 1st you have to prove that its curl should be 0 that it is rotational or conservative vector field if it is rotational then we can find its scalar potential means we can cancel out its gradient then we will fin ita work done so we will solve a question now we will find its curl on this topic, I have already uploaded one video here you can click on 'I' tab and go through the video of curl this f is irrotational if this is conservative vector field then we can find its scalar potential means we have to do its integration a gradient is a derivative cancel out the gradient means doing its integration I am telling you a short trick this you can do in exam also while doing integration variable should be separated this is scalar potential if you want to know that its is correct or not then you can take its gradient now we have to find its work done work done means doing its integration like these, we will solve this question let's take one more question same question as to the previous one an extra thing is that conservative vector field is given one last question on an independent path if we have to prove that it is independent of the path its is an irrotational or conservative vector field if it is irrotational or conservative vector filed means its integral is independent of its path same as the previous question nothing new the only language is changed I have already told this if anyone doesn't know before this go and watch line integral then you will get how to solve these like this way we will solve this question I have explained to you that what is an application of line integral my video sare coming on large scale all this video I have uploaded comment and share with your friends and press the notification bell so you get the notification of new video thank you so much for watching my video