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## Homework Statement

let F be vector field:

[tex]\[\vec F = \cos (xyz)\hat j + (\cos (xyz) - 2x)\hat k\] [/tex]

let L be the the curve that intersects between the cylinder [tex]\[(x - 1)^2 + (y - 2)^2 = 4

\][/tex] and the plane y+z=3/2

calculate:

[tex]\[\left| {\int {\vec Fd\vec r} } \right|\][/tex]

## Homework Equations

in order to solve this i thought of using the stokes theorem because the normal to the plane is [tex] \[\frac{1}{{\sqrt 2 }}(0,1,1)\] [/tex]

thus giving me

[tex]\oint{Fdr}=\int\int{curl(F)*n*ds}=\int\int{2/sqrt{2}*\sin(xyz)}[/tex]

i tried to parametries x y and z x= rcos(t)+1 y=rsin(t)+2 z=1/2-rsin(t)

but it wont work

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