Problem

PART 1: Fill in the blanks.

• Work need not be shown, only answers will be graded.

• 4 points for each blank and 100 points total.

• Each answer need to be clearly labeled on the answer sheet.

• Use of any device with computer algebra system during the exam will result in zero points.

20. The flux of the vector field $\vec{F}=(\sin y+x^3,3yz^2+e^z,3zy^2)$ through the surface $x^2+y^2+z^2=1,\ z\ge 0$, where the surface is equipped with the upward normal, is $\underline{\quad(25)\quad}$.