Let C be the smooth curve r(t) = (2 cos t)i + (2 sin t)j + (3

Question:

Let C be the smooth curve r(t) = (2 cos t)i + (2 sin t)j + (3 - 2 cos³ t)k, oriented to be traversed counterclockwise around the z-axis when viewed from above. Let S be the piecewise smooth cylindrical surface x² + y² = 4, below the curve for z ≥ 0, together with the base disk in the xy-plane. Note that C lies on the cylinder S and above the xy-plane. Verify Equation (4) in Stokes’ Theorem for the vector field F = yi - xj + x²k.