Use the Divergence Theorem to find the flux of F = xy^2i + x^2yj + yk outward through the surface of the region enclosed by the cylinder x^2 + y^2 = 1 and the planes z = 1 and z =-1.

generals336 2020-12-29 Answered
Use the Divergence Theorem to find the flux of F=xy2i+x2yj+yk outward through the surface of the region enclosed by the cylinder x2+y2=1 and the planes z = 1 and z =-1.
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

Aamina Herring
Answered 2020-12-30 Author has 85 answers
Step 1
Divergence Theorem.
Let F be a vector field whose components have continuous first partial derivatives and let S be a piecewise smooth oriented closed surface. The flux of F across S in the direction of the surfaces
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

Relevant Questions

asked 2022-01-18
The ratio of the number of blue sticks to the number of green sticks in a box was 4:1. When David took out some blue and sticks and replaced them with an equal number of green sticks, the ratio of the number of blue sticks to the number of green sticks became 3:1. If there were 185 green sticks in the box now, (a) find the total number of blue and green sticks in the box, (b) find the number of green sticks in the box at first.
asked 2021-03-05
Apply Green’s theorem to find the outward flux for the field
F(x,y)=tan1(yx)i+ln(x2+y2)j
asked 2021-01-19
Using the Divergence Theorem, evaluate SF.NdS, where F(x,y,z)=(z3ix3j+y3k) and S is the sphere x2+y2+z2=a2, with outward unit normal vector N.
asked 2022-01-16
Brad and Lena are recording their classmates' eye color for a statistics assignment. In Brad's class, 3 out of the 25 students have green eyes. In Lena's class, 2 out of the 20 students have green eyes. Which class has the greater ratio of green-eyed students to total students?
asked 2021-03-04

Use Green's Theorem in the form of this equation to prove Green's first identity, where D and C satisfy the hypothesis of Green's Theorem and the appropriate partial derivatives of f and g exist and are continuous. (The quantity grad g×n=Dng occurs in the line integral. This is the directional derivative in the direction of the normal vector n and is called the normal derivative of g.)
cFnds=D÷F(x,y)dA

asked 2021-02-25
Evaluate Cx2y2dx+4xy3dy where C is the triangle with vertices(0,0),(1,3), and (0,3).
(a)Use the Greens
asked 2021-02-25
Use Stokes' Theorem to evaluate CFdr where C is oriented counterclockwise as viewed from above.
F(x,y,z)=(x+y2)i+(y+z2)j+(z+x2)k,
C is the triangle with vertices (3,0,0),(0,3,0), and (0,0,3).