Evaluate the surface integral ∬SF⋅dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.F(x,y,z)=2xyi+3yzj+3zxkWhere S if the part of the paraboloid z=4−x^2−y^2 that lies above the square 0≤x≤3,0≤y≤1, and has upward orientation.

Question

Evaluate the surface integral ∬SF⋅dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.
F(x,y,z)=2xyi+3yzj+3zxk
Where S if the part of the paraboloid z=4−x^2−y^2 that lies above the square 0≤x≤3,0≤y≤1, and has upward orientation.

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Math
Calculus

Integration