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Advanced MathQ&A LibraryEvaluate 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) = yi − xj + 2zk, S is the hemisphere x2 + y2 + z2 = 4, z ≥ 0, oriented downwardStart your trial now! First week only $4.99!*arrow_forward*

Question

Evaluate the surface integral

S |

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) = yi − xj + 2zk, *S* is the hemisphere

x^{2} + y^{2} + z^{2} = 4, z ≥ 0, oriented downward

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