Use a parametrization to find the flux F•n do across the surface in the given direction. F= - xi - yj + 3z

Q: Use a parameterization to find the flux F•n do of F = z°i+ xj – 4zk in the outward direction (normal…

A: We have to find the flux ∬SF·ndσ of F=z2i+xj-4zk in the outward direction across the surface cut…

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: We can find volume by using washers method.

Q: For vector A = , calculate the surface integral (f, A · ds)

A: In this question, we find the surface integral for the given vector function A=<x2yz, xy2z,…

Q: Q) S = the part of the paraboloid z = 10-x^2-y^2 above z = 1 F = [x^3, xy, z] Find the flux of F…

A: Step:-1 Given that S is part of paraboloid z=10-x2-y2 above z=1 Since, given that z=10-x2-y2 and…

Q: use a parametrization to find the flux f f s F . n dsacross the surface in the specified direction.…

A: Consider the function: Given   F=4xi+4yj+2kSurface cut from the bottom of the paraboloid z=x2+y2 by…

Q: Find the flux of F(x,y,z) = sin(xyz) i+ xy j + ze*/5 k across the part of the cylinder y? + 2 z? = 4…

A: According to question,Fx,y,z= sin xyzi +xy j + z ex5 k,equation of cylinder,y2 + 2z2 =4planes, x = 1…

Q: sing the Divergence Theorem, find the outward flux of F = 2xy 21 + 2x 2yj+ 5xy k across the boundary…

A:

Q: Use Stokes' Theorem to find the line integral | (17 + 2y°)i + (w + =°)5 +(= + 2r*)k) • dř where C is…

A: Stokes' Theorem: Let S be a oriented smooth surface which is bounded by the curve C (simple closed,…

Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

A:

Q: Find the area of the surface with the following parametrization: u COS V Τ (u, υ) - u sin v u? 0<u<…

A:

Q: Use the divergence theorem to find the outward flux of F across the boundary of the region D. F=x'i-…

A:

Q: Use the Divergence Theorem to calculate the flux of Flacross SI where F = zi + yj + zxk|and Slis the…

A: Given that F=zi+yj+zxk And, The objective is to find the .

Q: Use a parametrization to find the flux I F.n do across the surface in the given direction. F= - xi -…

A:

Q: Find the flux of F (x, y, z) = 4.xi+ 4yj+ 2k outward (away from the z-axis) through the surface cut…

A: The field lines of a vector field F through surfaces with unit normal n, the angle from n to F is θ.…

Q: Evaluate the integral f. x'y°dy – x³y'dx, where C is the square determined by the lines x = 0, y =…

A: We have to evaluate the given integral.

Q: Find the parametrization r(t) = [x(t), y(t), z(t)] of the curve obtained by intersecting the…

A:

Q: Use Stokes' theorem to evaluate frotF. ds. F(x, y, z) = xyi + e²j + xy²k; S consists of the four…

A: To find- Use Stokes' theorem to evaluate ∫SrotF·dS, Fx, y, z = xyi + e2j + xy2k; S consists of the…

Q: Use a parameterization to find the flux | F.n do of F = 5xy i- 4z k outward (normal away from the…

A:

Q: Find the circulation of F= (y +z)i+(x +z?)j+(x² + y² )k around the curve C in the counterclockwise…

A:

Q: Find the center of mass, the moment of inertia about the coordinate axes, and the polar moment of…

A:

Q: Let F < xy, 6z, 3y Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of…

A: The given problem is to evaluate the line integral using stokes theorem, we have to find the limits…

Q: Evaluate the flux integral F.S where S is the surface given by 22 = a? + y?, 0 <z< 4, oriented…

A: The given problem is to evaluate the given flux integral of the given vector field over the given…

Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Evaluate the flux integral F-ds where Pis the part of the paraboloid -= 4-x -y above the xy plane…

A: Any integral which is to be evaluated at the surface is called the surface integral. Divergence…

Q: . Calculate the flux integral fF.n ds, where C is the positively oriented circle of radius 1…

A: Given function is, Fx,y=x,2y The formula for calculating the flux of the integral ∮F·nds is,…

Q: Use the divergence theorem to evaluate the flux of F(x, y, z) = 2xyi+ yzj+ z? k across the surface…

A: We will use Divergence theorem to evaluate the flux.

Q: Find the flux of F = 3zi + 5y? i+ 3x k out of the closed cone y = Væ2 + z2, with 0 < y < 1. flux =

A:

Q: Find the flow of the velocity field F = (y + z)i + xj - yk, where velocity is measured in meters per…

A:

Q: use a parametrization to find the flux f f s F . n dsacross the surface in the specified direction.…

A:

Q: Compute the flux of F= xi+yj+ z*k across the cone z =Vx2 + y? , 0szs1, in the downward direction.…

A: We have to find the flux in the downward direction.   Let us assume that x=rcosθ, y=rsinθ, z=r Then…

Q: Let F = Use Stokes' Theorem to evaluate / F. dī, where Cis the curve of intersection of the…

A:

Q: Find the outward flux across the domain D xi + yj + zk x2 +y? + z? F(x,v,z) = across the sphere x2…

A:

Q: Find the average of the function f(r,0)=r sin(0/2) over a disk of radius R centered at the origin.

A: Given function: f(r,θ)=r2*sinθ2Disk description: radius=R0 and center at the origin To find: Average…

Q: Find the outward flux of F= (x')i+(y²)}+(z²)k across the boundary of the region D, where D is the…

A:

Q: Calculate the flux integral f(2i + 2j + 2k) · dA where S is a disk of radius 5 in the plane æ + y +…

A: Given F=2i+2j+2k,radius=5 and x+y+z=1 plane

Q: Use cylindrical coordinates to evaluate the triple integral /// (æ – y) dV, where E is the solid…

A:

Q: Use the Divergence Theorem to calculate the outward flux of F = (r3 + y, y + z3, z3 + 23) across S:…

A:

Q: Find the equation of the tangent plane Pr to the surface S:r + y? + z? = 9 at (2, 1, –2) O Pr: 4x –…

A:

Q: Use Stoke’s Theorem to evaluate the line integral ∮C(x+z)dx +(x−y)dy +xdz. The curve C is the…

A:

Q: Use Stokes' theorem to evaluate V ×F· î dS where = (9y²z, 4xz, 2x²y²) and S is the paraboloid z = x²…

A: Step:-1 Stoke's Theorem:- ∬s∇×F→.n dS=∫F.dr Now, given that F→=9y2z, 4xz, 2x2y2 and paraboloid…

Q: Let F . F. dr, where Use Stokes' Theorem to evaluate C is the curve of intersection of the…

A: The given vector function: F→=&lt;xy,2z,3y&gt; To find ∫CF→.dr by using Stokes theorem. The Formula…

Q: Find the moment of mass from the x-axis for y = x In(x) – 3x and y density is equal to 0.37…

A:

Q: Let w = e dr + 6x dy + sin(r) dz be a one-form on R*. Find the line integral of w going…

A:

Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

A: Given surface, F=2xyi+2yzj2xzk           ...(1) Given plane, x+y+z=2a                ...(2) Where…

Q: Find the flux of F = (y +xz)i + (y + yz)j – (2x + z²)k upward through the first octant part of the…

A:

Q: Compute the line integral of the scalar function f(x, y, z) = 2x² + 8z ver the curve c(t) = (et, t2…

A:

Q: Find an equation for the plane through the origin such that the circulation of the flow field F = zi…

A:

Q: Define stokes theorem and evaluate the line integral SF.r'(s) ds where F = [4z, 2x, 2x], C: the…

A:

Q: Use a parametrization to find the flux •n do across the surface in the given direction. S 2 F= - 2xi…

A: We have to find the flux using parametrization.