Let C be the smooth curve r(t) (2 cos t)i (2 sin t)j (3 2 cos 3 t)k, oriented to be traversed counterclockwise around the z axis when viewed from above Let S be the piecewise smooth cylindrical surface x 2 y 2 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 x 2 k X N C 2 y

Question: Let C be the smooth curve r(t) = (2 cos t)i + (2 sin t)j + (3 - 2 cos 3 t)k, oriented to be

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. X N C. 2 y

X N C. 2 y

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