The net outward flux of the vector field F(x,y,z) = 3xy² i + x cos(z) j + z³ k across the surface solid bounded by the cylinder y² + z² = 1 and the planes x = -1 and x = 2 was calculated using the divergence theorem. The divergence of F is 3r², leading to a triple integral that evaluates to 3π + (3π/2). The correct approach involves ensuring the integrand accounts for the Jacobian when converting to polar coordinates.
PREREQUISITESStudents and professionals in mathematics, physics, and engineering who are working on vector calculus problems, particularly those involving flux calculations across surfaces.
myfunkymaths said:Homework Statement
calculate net outward flux of vector field F(x,y,z)=3xy^2 i +xcosz j +z^3k, across surface solid bounded by cylinder y^2 +z^2 =1
planes x=-1, x=2
Homework Equations
The Attempt at a Solution
my attempt was triple integral of divF=> 3*triple integral r^3
ended up getting an answer =3pi + (3pi/2)
is the answer i got correct?
thank you
You forgot to multiply by r when converting to polarDick said:No, I don't think so. 3r^2 is ok for an integrand. How did you do the rest?
ƒ(x) said:You forgot to multiply by r when converting to polar