4. For the vector field F(x, y, z) = (xy + z, yz + x, zx + y) and the surface S = {(x,y,z) E R³: x² + y² + z² = 25 and 3

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4 For The Vector Field F X Y Z Xy Z Yz X Zx Y And The Surface S X Y Z E R X Y Z 25 And 3 1 (13.56 KiB) Viewed 7 times

4. For the vector field F(x, y, z) = (xy + z, yz + x, zx + y) and the surface S = {(x,y,z) E R³: x² + y² + z² = 25 and 3 ≤z≤5), i.e., the portion of the sphere centered at zero of radius 5, verify the Stokes Theorem fas F-Tds=ffs (VXF) .nds, by evaluating both integrals (Hint. Note that aS(t) = (4cost, 4sint, 3)),0 sts 2πr.) (CLO4) (25 points).