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zmey
2 days ago
13

Suppose that surface σ is parameterized by r(u,v)=⟨ucos(3v),usin(3v),v⟩, 0≤u≤7 and 0≤v≤2π3 and f(x,y,z)=x2+y2+z2. Set up the sur

face 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 = 2pi/3 ∫ 0 7 ∫ 0 u^2+v^2 ∥∥∥ ∥∥∥dudv
Mathematics
1 answer:
tester [11.9K]2 days ago
6 0
It appears you've gathered most of the relevant information, but a critical element is missing. The surface represented is parameterized by... and has a normal vector corresponding to this representation with a specified norm. Thus, the integral of... is...
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