00:01
Hi, from the question given that f of x, y is equal to inner product of minus y square x y plus 3.
00:14
So, here we need to solve this integral closed integral over the region c f dot dr.
00:25
So, we need to evaluate this by using gauss divergence or stokes theorem or by using the polar coordinate for circle r is equal to 2 and r is equal to 4 cos theta.
00:52
So, here 2 is equal to 4 cos theta.
00:57
So, theta is equal to pi over 3.
01:01
Therefore, r is lies from 2 less than or equal to r is less than or equal to 4 cos theta and 0 is less than or equal to theta is less than or equal to pi over 3 and by using green's theorem.
01:14
So, by using green's theorem, w integral over the region r dou by dou x of x y plus 3 minus dou by dou y of minus y square dx dy.
01:37
Since by using green's theorem integral over the region c m dx plus n dy is equal to double integral dou n by dou x minus dou m by dou y times dx dy.
02:05
So, this is the general formula.
02:07
So, by using this we need to evaluate the above integral.
02:11
So, we have double integral over the region r y minus minus 2 y dx dy.
02:23
So, that is equal to double integral over the region r 3 y dx dy.
02:32
Now, by using polar coordinate x is equal to r cos theta and y is equal to r sin theta.
02:39
So, da is equal to dx dy which could be equal to r dr d theta...