{(x1, x2, x3) € R³ | x3 = 5 − x² − x², x3 ≥ 1}, a portion of a circular paraboloid. Endow S with the upward orientation

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X1 X2 X3 R X3 5 X X X3 1 A Portion Of A Circular Paraboloid Endow S With The Upward Orientation 1 (37.1 KiB) Viewed 52 times

{(x1, x2, x3) € R³ | x3 = 5 − x² − x², x3 ≥ 1}, a portion of a circular paraboloid. Endow S with the upward orientation (positive x3- component in a normal vector). Use Stokes' Theorem to compute du via a line integral, where w = x₂ cos(x3) dx₁ - x₁ sin(x3) dx₂ + €¹i¹₂ dx3.