Answer the following vector calculus problems. Be sure to solve all parts. Thank you!

4. The double cone 2x2 = y + 22 intersects the sphere x2 + y' + 22 = 12x -11 along two closed curves C, and C2. Let E, be the portion of the sphere with boundaries given by C1 and C2. Likewise, let E2 be the portion of the sphere with boundaries also given by Ci and C2. (a) (10 pts) Find parametrizations for C, and C2 that has counter-clockwise orienta- tion about the r-axis. (b) (15 pts) Find a parametrization for En and use it to determine the area of 21. (c) (15 pts) Find a parametrization for E2 and use it to determine the area of Ez . (d) (6 pts) Is E a portion of a graph of some function? Likewise, is E2 a portion of a graph of some function? (e) (14 pts) Compute the line integral S F . ds = fox'dx - zdy + ydz for both C1 and C2 . Determine the value of J F . ds - JC, F . ds . (f) (5 pts) Does your answer in part (e) change if you replace x2 with f(x, y, z)