Use the divergence theorem to evaluate the surface integral missing z = 0, and N is the outward unit normal for S. F. Nd.S where F = 2yi - zj +3æk, S is the surface comprised of the five faces of the unit cube 0 ≤x≤ 1,0 ≤y≤ 1,0 ≤ z ≤ 1,

Q: Compute F. dS, F = (0, 0, z²), for the oriented surface S parametrized by (u, v) = (u cos(v), u…

A:

Q: Use the Divergence Theorem to evaluate s F. ds where and S is the sphere x² + y² + z² = 4 oriented…

A: The Given function is , and the surface is  oriented by the outward normal.To Find: .

Q: Let D be any surface and let F = (P depends only on x, Q only on y, and R only on z). Then that…

A: We will use the stokes theorem to check if the statement is true.

Q: Evaluate the surface integral Leyds where S is the portion of the planer + y + z = 1 that lies in…

A: Let S be the portion of the function z=f(x,y) , then the surface integral over S is defined as…

Q: Evaluate || f (x,y,z) dS where S is the portion of the sphere centered at the origin of radius two…

A: we have the equation of sphere x2+y2+z2=22s is the portion bounded between xy plane and z=1 in the…

Q: Calculate the surface integral 1 (V × F) - dS where M is the hemisphere ² + y² + 2² = 9, π ≥ 0, with…

A:

Q: 21. Show that the volume V of a region D in space enclosed by the oriented surface S with outward…

A:

Q: Use the Divergence Theorem to evaluate / F. ds where and S is the boundary of the sphere x² + y² +…

A: The Given function is , and the surface is  oriented by the outward normal.To Find: .

Q: 4. Let S be the upward oriented cone (normal vectors always point in the positive z direction) z =…

A:

Q: How would you evaluate [[ F-dS, where S is the surface with param etrization G(4, v) with domain D?

A: We need to demonstrate the method of evaluating the surface integral. ∬SF.dS Where, parametrisation…

Q: Let F(z, y, 2) = (y, Y, z + z²), and let S'be the surface of a very small sphere centered at (-1,0,…

A: The sphere has the equation (x+1)2+y2+(z-1)2=r2, where r is the radius of sphere. If the sphere is…

Q: Consider the closed surface S consisting of the graph z = 1 - x2 - y2 with z 2 0, and also the unit…

A: Here, F(x,y,z)=(5x,5y,z) z=1-x2-y2 x2+y2+z=1

Q: Evaluate the surface integral fs F. dS where F = (-2x, –5z, 5y) and S is the part of the sphere x? +…

A:

Q: F.N= (b) Calculate the normal component of F to the surface at P = (1, 2, 9) = (2, 3). (Use symbolic…

A: Given:It is given that  and  is the oriented surface parameterized by  for  and .To Find:(a) We have…

Q: Assume S is a smooth surface parametrized by R(u,v) = (V / za sin y do. Evaluate S Hint: Find the…

A: We use double integral to solve this.

Q: Use the given information to find sin(s+t) cos s=3/5 and cos t=8/17, s and t in quadrant IV  sin…

A: In IV quadrant, trigonometric functions like sine, cosine, tan and cot are negative and cos,sec are…

Q: Consider the surface given in the xy plane below with the orientation of the boundary given by the…

A: We can observe from the figure that the plane passes through the x and y axes. Therefore, this plane…

Q: Evaluate the surface integral s F. dS where F = (-1, 2, -y) and S is the part of the sphere x² + y²…

A:

Q: Let S be the quadratic surface given by S = {(x, y, z) | z = 4x² - y², z ≥ 0}, oriented with the…

A: