Calculus
posted by Antonio .
find the flux of F=<0,y,z> across the parabolic sheet given by x=2y^2+2z^2+3, with x <= 5

Calculus 
MathMate
Flux = I = ∫∫F.n dS
for S over the surface, g(x,y,z), where
g(x,y,z) is the part of
x=2y²+2z²+3 where x≤5, which translates to
g(x,y,z)=x2y²2z²3
and the region is the part of the paraboloid where y²+z²≤1 after substitution of x≤5.
This region is circular with radius =1, which facilitates integration later.
Now:
F = <0,y,z>
n=∇g/g
so I can be evaluated:
I = ∫∫F.n dS
The surface integral can be evaluated by projecting it to the region R on the yz plane by multiplying:
dS over S = g dA over R
So
I = ∫∫F.n dS over S
= ∫∫F.n g dA over R
where R is the circular region r≤1 in polar coordinates.
The way I have defined g(x,y,z) results in negative flux.
Post if you could use more help.
Respond to this Question
Similar Questions

math (calculus)
A rectangular sheet of paper of width a and length b, where 0<a<b, is folded by taking one corner of the sheet and placing it at point P on the opposite long side of the sheet. The fold is flatened to form a crease across the … 
calculus
Find the tangential and normal components of acceleration of an object that moves along the parabolic path y=4x^2 at the instant the speed ds/dt=5. I know how to find the both these given a vector but no idea when given just a path … 
Physics
An infinite,insulating sheet has a surface charge density 3.14C/m^2 the height is 12km A.) find the surface area of the Gaussian surface B.) find the total charge C.) find the total electric flux D.) use Guass's law to find the electric … 
Calc
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i + y j + z4 … 
Calc
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = y i − x j + z2 … 
Calc
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xy i + yz j + zx … 
Calc
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xy i + yz j + zx … 
Calc 3
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i + y j + z4 … 
Math
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i + y j + z4 … 
mathIS MY ANSWER RIGHT?
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i + y j + z4 …