00:01
Let's have a look at the question.
00:03
So the question states, use stokes theorem to compute the flux of the curl of a vector field f vector is equals to 2x minus yi minus yz square j and minus y square zk.
00:23
Out of the rectangular parallel piped surface which has the range of x as from 0 to 3 then y is from 0 to 2 and z lies from 0 to 1 above the xoy plane.
00:42
So here we have the figure as this is z axis then here we have the y axis and this is the x axis and we have the figure here so this is our figure and this is the point o this is our shaded region.
01:17
Now here let us solve this using the stokes theorem.
01:21
So according to the stokes theorem to compute the flux out of the rectangular parallel piped surfaces we know that the stokes property is that integration over the closed surface c of f vector dr is equals to double integration over the surface s and delta cross product with f vector nds.
01:48
Now here delta cross product with f vector is given as here we have i, j and k then here we have d by dx d by dy and dy dz and here we have the values 2x minus y here we have minus y z square and here we have y square z.
02:16
So we will get this as i multiplied with minus 2 yz plus 2 yz minus j multiplied with 0 minus 0 and plus k multiplied with 0 minus minus 1.
02:36
So here we will get that del cross product with f vector is equals to k vector...