00:01
Hi, from the first screen given that we need to evaluate the given integral by using the green's theorem.
00:05
So, we closed integral over c 4y minus 2 comma 4x square minus 9 dot dr where c is the boundary of the rectangle with vertices.
00:17
So, let us consider the boundary of the rectangle 0 comma 0 and 2 comma 0 and 2 comma 4 and 0 comma 4.
00:35
So, it will form the boundary of the rectangle.
00:39
So, now by using green's theorem p is equal to 4y minus 2 and q is equal to 4x square minus 9.
00:49
So, dou p by dou y is equal to 4 and dou q by dou x is equal to 8x.
00:57
So, by using green's theorem closed integral over the region c p dx plus q dy is equal to double integral over the region r dou p sorry dou q by dou x minus dou p by dou y da.
01:17
So, here integral here first y x varies from 0 to 2 and y varies from 0 to 4 and dou q by dou x is 8x minus 4 da is dy dx.
01:40
So, on integrating this first integrate with respect to y...