HiAttached is the details of the problem, let me know if you have any question. Thanks,Best, James,

1) For cylindrical surface, the easiest coordinate to use is the polar coordinate with
y-axis perpendicular to the polar coordinate x-z plane, i.e., we have
x = rcos
z = rsin
y=y
then the unit vector n̂ of the cylindrical surface is r̂ p[oint away from y-axis, and the direction
point toward y axis is - r̂ , the cylindrical surface is just r=2. The upper limit of y is yu = 5- 4 =1,
the lower limit of y is simply the x-z plane i.e., y=0. rˆ  iˆ cos   kˆ sin  (note (r,) is in x-z
plane).
Then the require flux is

 

F

d
S
�...