This document asks to use the divergence theorem to find the double integral of F·n da, where F is the vector field (x^2+sinx)i + (y-xe-y)j + z^2k, over the surface S bounded by the cylinder x^2+y^2=4 and the planes x+z=2 and z=0.

1. Q7 Use the dicergence therorm to find
∬ 퐹. 푛푑퐴
푆
where 퐹 = (푥 2 + 푠푖푛푦푧)푖 + (푦 − 푥푒− 푧 )푗 + 푧^2푘 and S is the surface od the region bounded by
the cylinder: 푥 2 + 푦2 = 4 and the planes: 푥 + 푧 = 2 , 푧 = 0