00:01
So, let us start with the concept which we are going to use here for this question.
00:07
So, if you having given the integration pdx plus q d y of type of integral.
00:15
So, this can be written as double integration into the bracket partial differentiation of q with respect to x minus partial differentiation of p with respect to y into da and hence according to this we can write down that the integration of.
00:39
So, according to question if you see that what is q what is x.
00:44
So, you having given the close integration of 7x plus e to the power y square d y minus of 2y square plus arc tan means tan inverse of x square dx where c is the boundary of square whose vertices we having given as 4 comma 2 7 comma 2 7 comma 5 and 4 comma 5.
01:16
So, we have to find the required solution of this.
01:19
So, on comparing you will get this is nothing but what representing the q term and this is what representing the p term.
01:28
So, let us find del q by del x.
01:32
So, we are differentiating with respect to x that is why the differentiation will be 7 while for this e to the power y square will be going to 0.
01:41
Similarly, del p del y will be gives to d 2 to the 4 and this negates then will get inside.
01:50
So, will become minus of 4 y.
01:54
So, i am storing this above in the required formula.
01:58
So, this should be the double integrations.
02:01
What was that? del q by del x minus del p by del y...