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Use Stokes' Theorem to evaluate S ∫ F · dS. F(x, y, z) = x2 sin(z)i + y2j + xyk, S is the part of the paraboloid z = 4 − x2 − y2 that lies above the xy-plane, oriented upward.

User Induane
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Answer:

Look at the image,

Explanation:

This is an explanation of the same exercise but when the paraboloid is z = 9 − x2 − y2. In that case you just have to replace 9 by 4 and follow the same steps :).

Use Stokes' Theorem to evaluate S ∫ F · dS. F(x, y, z) = x2 sin(z)i + y2j + xyk, S-example-1
User VeeDuvv
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