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Mathematics, 15.07.2019 06:30 danidavis2002
Verify stokes' theorem for the helicoid ψ(r,θ)=⟨rcosθ,rsinθ,θ⟩ where (r,θ) lies in the rectangle [0,1]×[0,π/2], and f is the vector field f=⟨6z,8x,8y⟩. first, compute the surface integral: ∬m(∇×f)⋅ds=∫ba∫dcf(r,θ)drdθ, where a= , b= , c= , d= , and f(r,θ)= (use "t" for theta). finally, the value of the surface integral is . next compute the line integral on that part of the boundary from (1,0,0) to (0,1,π/2). ∫cf⋅dr=∫bag(θ)dθ, where a= , b= , and g(θ)=
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Verify stokes' theorem for the helicoid ψ(r,θ)=⟨rcosθ,rsinθ,θ⟩ where (r,θ) lies in the rectangle [0,...
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