Question

In: Advanced Math

Verify Stokes theorem for F =(y^2 + x^2 - x^2)i + (z^2 + x^2 - y^2)j...

Verify Stokes theorem for F =(y^2 + x^2 - x^2)i + (z^2 + x^2 - y^2)j + (x^2 + y^2 - z^2)k over the portion of the surface x^2 + y^2 -2ax + az = 0

Solutions

Expert Solution


Related Solutions

Verify stokes theorem when S=(x,y,z): 9x^2+y^2=z^2 and 0 ≤z ≤2 and F(x,y,z)=0i+((9x^2)/2)j+((y^(3)*z)/3)k
Verify stokes theorem when S=(x,y,z): 9x^2+y^2=z^2 and 0 ≤z ≤2 and F(x,y,z)=0i+((9x^2)/2)j+((y^(3)*z)/3)k
Verify stokes theorem when S=(x,y,z): 9x^2+y^2=z^2 and 0 ≤z ≤2 and F(x,y,z)=0i+((9x^2)/2)j+((y^(3)*z)/3)k
Verify stokes theorem when S=(x,y,z): 9x^2+y^2=z^2 and 0 ≤z ≤2 and F(x,y,z)=0i+((9x^2)/2)j+((y^(3)*z)/3)k
Verify the Divergence Theorem for the vector field F(x, y, z) = < y, x ,...
Verify the Divergence Theorem for the vector field F(x, y, z) = < y, x , z^2 > on the region E bounded by the planes y + z = 2, z = 0 and the cylinder x^2 + y^2 = 1. By Surface Integral: By Triple Integral:
Verify the Divergence Theorem for the vector eld F(x; y; z) = hy; x; z2i on...
Verify the Divergence Theorem for the vector eld F(x; y; z) = hy; x; z2i on the region E bounded by the planes y + z = 2, z = 0 and the cylinder x2 + y2 = 1. Surface Integral: Triple Integral:
Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find the...
Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find the flux of F across S, the part of the paraboloid x2 + y2 + z = 29 that lies above the plane z = 4 and is oriented upward.
Use the Stoke’s theorem to evaluate Z Z S (∇×F)·nˆ·dS where F(x, y, z) = (x^2...
Use the Stoke’s theorem to evaluate Z Z S (∇×F)·nˆ·dS where F(x, y, z) = (x^2 z^2,y^2 z^2, xyz) and surface S is part of the paraboloid z = x^2 + y^2 that lies inside the cylinder x^2 + y^2 = 4, oriented upwards. Sketch the surface S and label everything.
Consider F and C below. F(x, y, z) = 2xz + y2 i + 2xy j...
Consider F and C below. F(x, y, z) = 2xz + y2 i + 2xy j + x2 + 6z2 k C: x = t2,    y = t + 2,    z = 3t − 1,    0 ≤ t ≤ 1 (a) Find a function f such that F = ∇f. f(x, y, z) = x2z+xy2+2z3+c     (b) Use part (a) to evaluate    C ∇f · dr along the given curve C.
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 + 14z) k C is the line segment from (3, 0, −1) to (6, 4, 2) (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.
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 + 14z) k C is the line segment from (3, 0, −3) to (5, 5, 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.
Consider F and C below. F(x, y, z) = 2xz + y2 i + 2xy j...
Consider F and C below. F(x, y, z) = 2xz + y2 i + 2xy j + x2 + 15z2 k C: x = t2,    y = t + 2,    z = 4t − 1,    0 ≤ t ≤ 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.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT