Mathematics, 20.12.2019 19:31 rjennis002
Suppose that surface σσ is parameterized by r(u, v)=⟨ucos(6v),usin(6v),v⟩r(u, v)=⟨ucos(6v),usin(6v),v⟩, 0≤u≤70≤u≤7 and 0≤v≤1π30≤v≤1π3 and f(x, y,z)=x2+y2+z2f(x, y,z)=x2+y2+z2. set up the surface integral (you don't need to evaluate it). ∫σ∫f(x, y,z)ds=∫r∫f(x(u, v),y(u, v),z(u, v))∥∥∥∂r∂u×∂r∂v∥∥∥da∫σ∫f(x, y,z)ds=∫r∫f(x(u, v),y(u, v),z(u, v))‖∂r∂u×∂r∂v‖da
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Suppose that surface σσ is parameterized by r(u, v)=⟨ucos(6v),usin(6v),v⟩r(u, v)=⟨ucos(6v),usin(6v),...
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