00:01
Hi here for the given question.
00:03
We are given that filled f is equal to x square plus sine z comma xy plus cos z and e y.
00:13
So this is the vector field f now here we need to calculate value of flux.
00:17
So flux can be written as double integration over s f dot and ds which is equivalent to triple integration over region q divergence of f multiplied with dv.
00:28
So here first of all, we will calculate the value of divergence of f which is equal to del upon del x comma del upon del y comma del upon del z for the value of f, which is x square plus sine z comma xy plus cos z comma e to the power y.
00:50
So calculating this value we have divergence of f is equal to 2x plus x plus 0 which is equal to 3x.
00:58
So this is the divergence of f.
00:59
So here in our case the value of flux can be written as triple integration over region q 3x dv.
01:07
Now here we can observe that this is the region over the disk.
01:11
So here we can say that we have double integration over disk and here integration over 0 to 6 minus x.
01:18
Here we have 3x dz da.
01:21
So here in our case double integration over disk as it is and here changing into the polar coordinate.
01:27
We can write this as here.
01:30
We have 16 x 18 x minus 3 x square da by integrating this term with respect to 3x.
01:38
So here in our case further if we change the terms into polar coordinate, we have a double integration over disk as it is here.
01:46
We have 18 r cos theta minus 3r square cos square theta...