Net Outward Flux of Vector Field Across Surface Solid

[myfunkymaths]

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

 

[ƒ(x)]

did not work out the integral, but your approach seemed correct. there's this handy site called wolfram alpha you know...it evaluates integrals and (i haven't checked) might even do flux.

 

[Dick]

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

No, I don't think so. 3r^2 is ok for an integrand. How did you do the rest?

 

[ƒ(x)]

No, I don't think so. 3r^2 is ok for an integrand. How did you do the rest?

You forgot to multiply by r when converting to polar

 

[Dick]

You forgot to multiply by r when converting to polar

I didn't quite forget. I meant 3r^2 for div(F). Sure, it becomes 3r^3 with the extra factor of r from the area element. Thanks.

 

[myfunkymaths]

ok, thanks for the comments.