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Evaluate the surface integral S F · dS for the given vector field F and the...

Evaluate the surface integral S F · 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) = x2 i + y2 j + z2 k S is the boundary of the solid half-cylinder 0 ≤ z ≤ 25 − y2 , 0 ≤ x ≤ 3

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