Dear Krithika,

Your score in Exam 2 is 83 out of 100

Everything was right except

#1: started the right (but too complicated way, see the answer key for the good way)
but then did very serious integration errors: -7 points

#2: right way, wrong answer (cos(0) is 1 not 0): -2 points

#5: wrong answer, partially right way. The integration is over the part of
the sphere that is x,y,z>0 NOT the whole sphere: -5 points

#9: no final answer (it wasn't that hard), more seriously, did not multiply by -1
thins the direction is DOWNWARD: -4 points



Best wishes,

  Dr. Z.