Question

Let F = x²i + (9xy + x)j + zk. Let C be the circle x² + y² = 1 and S the disc x² + y² ≤ 1 within the plane z = 0

13. -/3 points MarsVectorCalc6 8.2.031 Let F = x21+ (9xy + x)j + zk. Let C be the circle x2 + y2-1 and S the disc x2 + y2 S 1 within the plane z = o. (a) Determine the flux of F out of S. (b) Determine the circulation of F around C. (c) Find the flux of ▽ x F. Verify Stokes' theorem directly in this case.

Show transcribed image text 13. -/3 points MarsVectorCalc6 8.2.031 Let F = x21+ (9xy + x)j + zk. Let C be the circle x2 + y2-1 and S the disc x2 + y2 S 1 within the plane z = o. (a) Determine the flux of F out of S. (b) Determine the circulation of F around C. (c) Find the flux of ▽ x F. Verify Stokes' theorem directly in this case.