Let F vector = <x,y,z> and use the Divergence Theorem to calculate the (nonzero) volume of some solid in IR3 by calculating a surface integral. (You can pick the solid).

Amari Flowers 2021-01-10 Answered
Let Fr=<x,y,z> and use the Divergence Theorem to calculate the (nonzero) volume of some solid in IR3 by calculating a surface integral. (You can pick the solid).
You can still ask an expert for help

Want to know more about Green's, Stokes', and the divergence theorem?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Cristiano Sears
Answered 2021-01-11 Author has 96 answers
Step 1
Consider the provided question,
Given, F=x,y,z=ξ+yj+zk
Let s be a closed surface enclosing some volume V.
Find sFNds
By gauss divergence theorem,
sFNds=V÷Fdv
Since, F=ξ+yj+zk
div F=x(x)+(y)(y)+(z)(z)
=1+1+1
=3
Step 2
Now, find the (nonzero) volume V of some solid in R3 by calculating a surface integral.
sFNds=V÷Fdv
=V(3)dv
=3V1dv
sFNds=3V
V=1.3sFNds
Hence, nonzero volume, V=13sFNds
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more