Question

Evaluate using Stokes' theorem: a) ∬ ∇ × ? ∙ ???, if F = (xy, yz,...

Evaluate using Stokes' theorem: a) ∬ ∇ × ? ∙ ???, if F = (xy, yz, xz) in a cylinder z = 1-x two for 0≤ x ≤1, -2 ≤y ≤2

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Use Stokes" Theorem to evaluate (F-dr where F(x, y, z)=(-y , x-z , 0) and the...
Use Stokes" Theorem to evaluate (F-dr where F(x, y, z)=(-y , x-z , 0) and the surface S is the part of the paraboloid : z = 4- x^2 - y^2 that lies above the xy-plane. Assume C is oriented counterclockwise when viewed from above.
1. a) For the surface f(x, y, z) = xy + yz + xz = 3,...
1. a) For the surface f(x, y, z) = xy + yz + xz = 3, find the equation of the tangent plane at (1, 1, 1). b) For the surface f(x, y, z) = xy + yz + xz = 3, find the equation of the normal line to the surface at (1, 1, 1).
Use Stokes' Theorem to evaluate    S curl F · dS. F(x, y, z) = x2...
Use Stokes' Theorem to evaluate    S curl F · dS. F(x, y, z) = x2 sin(z)i + y2j + xyk, S is the part of the paraboloid z = 1 − x2 − y2 that lies above the xy-plane, oriented upward.
Consider F and C below. F(x, y, z) = yz i + xz j + (xy...
Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 18z) k C is the line segment from (1, 0, −3) to (4, 4, 1) (a) Find a function f such that F = ∇f. f(x, y, z) = (b) Use part (a) to evaluate C ∇f · dr along the given curve C.
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed...
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = 5yi + xzj + (x + y)k, C is the curve of intersection of the plane z = y + 7 and the cylinder x2 + y2 = 1.
Consider F and C below. F(x, y, z) = yz i + xz j + (xy...
Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 12z) k C is the line segment from (2, 0, −3) to (4, 6, 3) (a) Find a function f such that F = ∇f. f(x, y, z) =       (b) Use part (a) to evaluate    C ∇f · dr along the given curve C.
Let F(x, y, z) = (yz, xz, xy) and the path c(t) = (cos3 t,sin3 t,...
Let F(x, y, z) = (yz, xz, xy) and the path c(t) = (cos3 t,sin3 t, 0) for 0 ≤ t ≤ 2π. Evaluate R c F · ds. Hint: Identify f such that ∇f = F.
Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2 sin(z)i...
Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2 sin(z)i + y2j + xyk, S is the part of the paraboloid z = 1 − x2 − y2 that lies above the xy-plane, oriented upward.
Use Stokes' Theorem to evaluate the surface integral ∬ G curl F ⋅ n d S...
Use Stokes' Theorem to evaluate the surface integral ∬ G curl F ⋅ n d S where F ( x , y , z ) = ( z 2 − y ) i + ( x + y z ) j + x z k , G is the surface G = { ( x , y , z ) | z = 1 − x 2 − y 2 , z ≥ 0 } and n is the upward...
Let F(x, y, z) = 4yz, 5xy, 2xz . Apply Stokes' Theorem to evaluate C F...
Let F(x, y, z) = 4yz, 5xy, 2xz . Apply Stokes' Theorem to evaluate C F · dr by finding the flux of curl(F) where C is the square with vertices (0, 0, 2), (1, 0, 2), (1, 1, 2), and (0, 1, 2) oriented counterclockwise as viewed from above.