= The appropriate vector normal to the plane z = 8 – 4.x – 2y is (-22, –Zy, 1) = (4,2,1), which points upward, consisten

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The Appropriate Vector Normal To The Plane Z 8 4 X 2y Is 22 Zy 1 4 2 1 Which Points Upward Consisten 1 (53.64 KiB) Viewed 29 times

Can someone explain this calculation step by step. I am confused
on how the answer was reached. Such as finding R and the
calculation within the integral.
THank you
= The appropriate vector normal to the plane z = 8 – 4.x – 2y is (-22, –Zy, 1) = (4,2,1), which points upward, consistent with the orientation of C. The triangular region R in the xy-plane beneath S is found by setting z = 0 in the equation of the plane; we find that R= {(x, y): 0 < x < 2,0 Sy < 4 – 2x}. The surface integral in Stokes' Theorem may now be evaluated: Substitute and convert to a double integral over R. R SS (V x F) ·n ds = SS (1 – 2y, 1 – 2x,0) · (4, 2, 1)dA S (1 – 2y, 1 – 2:0, 0) 4-23 = SƏ S. 1–24 (6 – 4x – 8y)dy dx = Simplify. Evaluate integrals. 88