I got x is less than or equal to 3
By the divergence theorem, the surface integral over
is
where
denotes the space bounded by
. Assuming the vector field is given to be
then
Converting to spherical coordinates, we take
so that the triple integral becomes
Now the integral over
alone will be the difference of the integral over
and the integral over
, i.e.
We can parameterize the points in
by
so that the integral over
is
So, the integral over
alone evaluates to
It would be good if you add the answers choice, but I guess it’s (b/2)^2
Answer:
14
f(x) = 7
-7^2 + 9(7)= -49 + 63 = 14