Question

In: Advanced Math

1A) Use surface integral to evaluate the flux of F(x,y,z) =<x^3,y^3,z^3> across the cylinder x^2+y^2=1, 0<=z<=2...

1A) Use surface integral to evaluate the flux of
F(x,y,z) =<x^3,y^3,z^3>
across the cylinder x^2+y^2=1, 0<=z<=2

1B) Use the Divergence Theorem to evaluate the flux of F(x,y,z) =<x^3,y^3,z^3>

across the cylinder x^2+y^2=1, 0<=z<=2

Solutions

Expert Solution


Related Solutions

Compute the derivative of the given vector field F. Evaluate the line integral of F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )
Compute the derivative of the given vector field F. Evaluate the line integral of F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )over the path C consisting of line segments joining (1,1,1) to (1,1,2), (1, 1, 2) to (1, 3, 2), and (1, 3, 2) to (4, 3, 2) in 3 different ways, along the given path, along the line from (1,1,1) to (4,3,2), and finally by finding an anti-derivative, f, for F.
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.
Use spherical coordinates to evaluate the triple integral ∭e^−(x^2+y^2+z^2)/(x^2 + y^2 + z^2) dV , Where...
Use spherical coordinates to evaluate the triple integral ∭e^−(x^2+y^2+z^2)/(x^2 + y^2 + z^2) dV , Where E is the region bounded by the spheres x^2 + y^2 + z^2 = 4 and x^2 + y^2 + z^2 = 9
Given function f(x,y,z)=x^(2)+2*y^(2)+z^(2), subject to two constraints x+y+z=6 and x-2*y+z=0. find the extreme value of f(x,y,z)...
Given function f(x,y,z)=x^(2)+2*y^(2)+z^(2), subject to two constraints x+y+z=6 and x-2*y+z=0. find the extreme value of f(x,y,z) and determine whether it is maximum of minimum.
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
Compute the line integral of the vector field F(x, y, z) = ⟨−y, x, z⟩ along...
Compute the line integral of the vector field F(x, y, z) = ⟨−y, x, z⟩ along the curve which is given by the intersection of the cylinder x 2 + y 2 = 4 and the plane x + y + z = 2 starting from the point (2, 0, 0) and ending at the point (0, 2, 0) with the counterclockwise orientation.
1.Evaluate the integral C where C is x=t^3 and y=t, 0 ≤ t ≤ 1 2.Find...
1.Evaluate the integral C where C is x=t^3 and y=t, 0 ≤ t ≤ 1 2.Find the area of the surface with vectorial equation r(u,v)=<u,u sinv, cu >, 0 ≤ u ≤ h, 0≤ v ≤ 2pi
Let F(x,y,z) = < z tan-1(y2), z3 ln(x2 + 1), z >. Find the flux of...
Let F(x,y,z) = < z tan-1(y2), z3 ln(x2 + 1), z >. Find the flux of F across S, the top part of the paraboloid x2 + y2 + z = 2 that lies above the plane z = 1 and is oriented upward. Note that S is not a closed surface.
Mystery(y, z: positive integer) 1 x=0 2 while z > 0 3       if z mod 2...
Mystery(y, z: positive integer) 1 x=0 2 while z > 0 3       if z mod 2 ==1 then 4                x = x + y 5       y = 2y 6       z = floor(z/2)           //floor is the rounding down operation 7 return x Simulate this algorithm for y=4 and z=7 and answer the following questions: (3 points) At the end of the first execution of the while loop, x=_____, y=______ and z=_______. (3 points) At the end of the second execution of...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT