00:01
So to solve this problem, we have been given vector f equal to x, y, z, comma, x, y, comma, x over 2, y, z.
00:22
So first we need to find curl f.
00:34
So curl f is equal to i z and k, dale, dail y, del x, del, dail x, del y, dill, dail g, x, x, y, x, y, dyl, dyl, dyl g, x, x, x, x y x over 2 y z when we solve it we get x square z i cap minus 2x y z minus x y z minus x y k cap when we yes sir? f tall f d s equal to fdr equal to s1 call f d s equal to s2 call fds so we get call f equal to f dot k equal to y minus xg so to find the value by using the boundary limits we get in second part call f d d x square multiply minus 4 comma x y minus 2 xy minus 4 comma y minus x multiply minus 4 so domain over x y x is greater than equal to minus 5 less than equal to minus 2 as to limit call f dot d s2 equal to d x square g comma x y minus 2 xy minus 2xy comma y minus x g so substitute z equal to minus 5 minus 5 x square comma x y plus 10 x y plus 10 x d r so when we solve it we get minus 5 by minus 25 x d r so now we can substitute the minus 5 to minus 2 minus 5 to minus 2 minus 2 minus 2 minus 5y, minus 25x...