Question

Help Entering Answers 1 point) Verify that Stokes' Theorem is true for the vector field F that lies above the plane z1, oriented upwards. 2yzi 3yj +xk and the surface S the part of the paraboloid z 5-x2-y To verify Stokes' Theorem we will compute the expression on each side. First computecurl F dS curl F0,3+2y,-2 Edy dx curl F dS- where x2 = curl F ds- Now compute F.dr The boundary curve C of the surface S can be parametrized by: r(t2 cos() (Use the most natural parametrization) F dr dt F dr ut. Help Entering Answers (1 point) Use Stokes' Theorem to evaluate (3xyi - 2zj + 3yk) dr where C is the intersection of the plane x z5 and the cylinder x2 y 9 oriented counterclockwise as viewed from above Since the ellipse is oriented counterclockwise as viewed from above the surface we attach is oriented 5 Usng this surface in Stokes Theorem evaluate The easiest surface to attach to this curve is the interior of the cylinder that lies on the plane x + z the following F-dr = where ti Evaluate F.dr

Answer 1