Use the Divergence Theorem to calculate the surface integral int int_S F · dS, that is, calculate the flux of F across S. F(x, y, z) = (x^3 + y^3)i + (y^3 + z^3)j + (z^3 + x^3)k, S is the sphere with center the origin and radius 2.

Anish Buchanan 2021-01-31 Answered
Use the Divergence Theorem to calculate the surface integral SF·dS, that is, calculate the flux of F across S.
F(x,y,z)=(x3+y3)i+(y3+z3)j+(z3+x3)k, S is the sphere with center the origin and radius 2.
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

Bentley Leach
Answered 2021-02-01 Author has 109 answers
Let E be a simplesolid region and S is the boundary surface of E with positive orientation and Let F be a vector field whose components have continous first orderpartial derivatives. then
SFdS=E÷FdV
Step 2
Apply the above theorem as follows.
Given that F(x,y,z)=(x3+y3)i+(y3+z3)j+(z3+x3)k
div F=F=3x2+3y2+3z2
SFdS=EidvFdV
=E(3x2+3y2+3z2)dV
=3E(x2+y2+z2)dV
=36E(2)dVx2+y2+z2=22)
=72E1dV
=72(4π3×23) ( volume of the sphere is 4π3r3)
=768π
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

You might be interested in

asked 2021-11-14
The half-life of C-14 is about 5730 yr.
a) Archaeologists find a piece of cloth painted with organic dyes. Analysis of the dye in the cloth shows that only 77% of the C-14 originally in the dye remains. When was the cloth painted?
b) A well-preserved piece of wood found at an archaeological site has 6.2% of the C-14 that it had when it was alive. Estimate when the wood was cut.
asked 2021-09-03
Let X1,X2,s˙,Xn be n independent random variables each with mean 100 and standard deviation 30. Let X be the sum of these random variables. Find n such that Pr(X>2000)0.95
asked 2021-09-12
If z and z are conjugate complex numbers , find two complex numbers, z=z1  and  z=z2 , that satisfy the equation 3zz+2(zz)=39+j12
asked 2022-01-25
Write a multivariable function (i.e z=f(x,y)) for a linear function that contains the points (−1,0),(0,2),(1,−1). Ive
asked 2021-01-13

Average value over a multivariable function using triple integrals. Find the average value of F(x,y,z)=x2+y2+z2 over the cube in the first octant bounded bt the coordinate planes and the planes x=5, y=5, and z=5

asked 2021-11-15
Equilibrium Price: Skateboards
The demand for your factory-made skateboards, in weekly sales, is
q=7p+50
If the selling price is $p. If you are selling them at that price, you can obtain
q=3p30
Per week from the factory. At what price should you sell your skateboards so that there is neither a shortage nor a surplus? (Round your answer to the nearest cent.)
asked 2021-03-01
Use Green's Theorem to evaluate CFdr where F(x,y)=xy2i+(1xy3)j and C is the parallelogram with vertices (-1,2), (-1,-1),(1,1)and(1,4).
The orientation of C is counterclockwise.

New questions