Verify the Stoke's theorem

[Hhhaaa]

Verify the Stoke's theorem where ?=(?,?,?) and ? is the part of the cylinder
?2+?2=1
cut off by the planes
?=0
and
?=?−4
oriented with normal ?⃗ pointing outward.

 

[Deleted member 4993]

Verify the Stoke's theorem where ?=(?,?,?) and ? is the part of the cylinder
?2+?2=1
cut off by the planes
?=0
and
?=?−4
oriented with normal ?⃗ pointing outward.

I can't decipher your post - specifically the equations. May be post a picture of your assignment.

 

[HallsofIvy]

It is not clear to me whether you mean specifically the "Cartan-Stokes theorem", that, given a vector valued function, \(\displaystyle \vec{F}\), \(\displaystyle \int\int_{\Sigma}\nabla\times \vec{F}\cdot d\vec{a}= \int_{\partial \Sigma} \vec{F}\cdot d\vec{l}\)​

or the "generlizied Stokes theorem" in the form of the "divergence theorem" that
\(\displaystyle \int\int\int_V \nabla\cdot\vec{F}dV= \int\int_{\partial V} \vec{F}\cdot d\vec{S}\).