Use Stokes' Theorem to evaluate ∫∫S curl F · dS. F(x,y,z) = exycos(z) i + x^2z j + xy k S is the hemisphere x = sqrt(25-y^2-z^2), oriented in the direction of the positive x-axis.
Added by Shelby S.
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We can parameterize this surface using spherical coordinates as follows: r(θ, φ) = (5cos(θ)sin(φ), 5sin(θ)sin(φ), 5cos(φ)) for 0 ≤ θ ≤ 2π and 0 ≤ φ ≤ π/2. Show more…
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