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27.11.2019 •
Mathematics
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 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 = 2pi/3 ∫ 0 7 ∫ 0 u^2+v^2 ∥∥∥ ∥∥∥dudv
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Ответ:
Looks like you have most of the details already, but you're missing one crucial piece.
is parameterized by
for and , and a normal vector to this surface is
with norm
So the integral of is
Ответ:
86 degrees fahrenheit
Step-by-step explanation: