Conservative Vector Fields . Surface Integrals Here are some example problems. This is not everything that is on the exam (obviously), but it is a good place to start. 1. Evaluate 42yr' (1 + ry?)'dA where R is the rectangular region (0, 1) x (0,2]. 2. Evaluate I' sin(y') dA where R is the region in the second quadrant bound by y = 3-,y = 12, and the y-axis. 3. Evaluate 4. Evaluate 5. Evaluate 2023 dv where E is the region bounded by 1 = 2- y' - 2 and z = by' + 523 -6. 6. Evaluate 2 dV where E is the region bounded by y - z? + 23 -4 and y - 8 - 512 - 52- with 7. Evaluate 2'dV where E is the region between the spheres r" ty t ? = 4 and rty +2 - 25. 8. Evaluate 9. Evaluate 12 - 2yds where ( is given by r(t) = (4t', t') for -1 S t 50. 10. Evaluate I + yds where C is given by the line segment from (-1, 0) towards (1, 0) adjoined by the northern semicircle of radius I oriented counterclockwise