Mathematics, 18.02.2020 18:03 alexkrol10
Use Stoke's Theorem to evaluate∬M(∇×F)⋅dS∬M(∇×F)⋅dS where MM is the hemisphere x2+y2+z2=4,x≥0x2+y2+z2=4,x≥0, with the normal in the direction of the positive x direction, and F=⟨x9,0,y2⟩F=⟨x9,0,y2⟩. Begin by writing down the "standard" parametrization of ∂M∂M as a function of the angle θθ (denoted by "t" in your answer) x=x= , y=y= , z=z= . ∫∂MF⋅ds=∫2π0f(θ)dθ∫∂MF⋅ds=∫02πf(θ)d θ, where f(θ)=f(θ)= (use "t" for theta). The value of the integral is.
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Use Stoke's Theorem to evaluate∬M(∇×F)⋅dS∬M(∇×F)⋅dS where MM is the hemisphere x2+y2+z2=4,x≥0x2+y2+z...
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