4. Use Stokes' Theorem to evaluate curl F · dS when F = ze i+ x cos yj+ xz sin y k and S is the hemi-sphere x? + y? + z? = 16,y 2 0. 5. Use the Divergence Theorem to calculate the surface integral , F dS: (a) F = xze i + xz²y³j – ze'k and S is the surface of the box bounded by the coordinate planes and the planes x = 2, y = 3 and z = 1.

Q: 23. Use Stokes' theorem to evaluate Se F · dr, where F(x, Y, z) = (xy, yz, zar) and C is the…

A:

Q: 4. Use the divergence theorem to evaluate the surface integral F dS where F - xzi + yzj + z?k and S…

A: we will use gauss divergence theorem here.

Q: Use the surface integral in Stokes Theorem to calculate the flux of the curl of the field F = 5zi +…

A: Stoke' s theorem ∫CF.dr =∫∫scurl F .ds Given  F=5z , x , 2y  and r =r cosθ , r sinθ , 25-r2   ;…

Q: The outflow of the field F(x,y,z)=(e^y−xz^2,x−yx^2,y−zy^2), across the edge of the solid contained…

A:

Q: 5. Use the Divergence Theorem to calculate the surface integral SF dS, where F(x, y, z) = (xye , xy?…

A: By divergence theorem value of the surface integral is

Q: 1. Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around…

A: Circulation of vector field F along curve C  =∫CF→dr→ According to stokes theorem…

Q: use the surface integral in Stokes’ Theorem to calculate the circulation of the field F around the…

A:

Q: 388. Use the divergence theorem to calculate surface integral F. dS when F(x, y, z) = ztan-1 (y²) i…

A: According to the divergence theorem, The surface-integral of a vector F, which is continuous and has…

Q: 1- Calculate the surface integral ffs G(r)dA, where G = (1+z2)} and S is given by the…

A: 1.  G=1+92xz12 ru,v=u,v,2u3 G(r)=1+92u.2u312 o≤u≤2, 0≤v≤2 is the limit of the integration.…

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

A:

Q: 7. Evaluate the line integral f, F· dr where F(x,y, z) = x³i – y²j+ zk and C is the x2 + 2xy + y²…

A:

Q: Use Green’s Theorem to evaluate around the boundary curve C of the region R, where R is the triangle…

A: According to the given information, it is required to calculate the work done by the force field

Q: 1. Use the divergence theorem to evaluate the surface integral F · dS, S where the vector field is F…

A:

Q: 4. Use the divergence theorem to evaluate the surface integral F. dS where F = xzi + yzj + z²k and S…

A:

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 4zi +…

A: The given question can be solved as shown in step2

Q: Let S: x2 + y? = 9,0szS7 be the surface of a closed cyllnder bounding a volume T.F=Ly², x², z²J. Use…

A:

Q: Use Stokes' theorem to calculate JJ (A) nds by A = 3yi-xzi+yz²k where S is the surface of the…

A: The given vector field is: A=3yi-xzj +yz2k The surface S is the paraboloid 2z=x2+y2 bounded by z=2.…

Q: use the surface integral in Stokes’ Theorem to calculate the circulation of the field F around the…

A:

Q: #5. Use Stokes' Theorem to evaluate curl F· dS, where F(x,y,z)= x (sin z)i+ y²j+xyk and S is the…

A:

Q: Use a CAS and Stokes' theorem to evaluate curl(F) · dS, where F(x, y, z) = 2yi + ej - arctan(x)k…

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: 387. Use the divergence theorem to calculate surface integral F. dS when F(x, y, z) = x²z³i+ 2xyz³j+…

A: Given that: F(x,y,z)=x2z3i+2xyz3j+xz4k and S is the surface of the box with vertices (±1,±2,±3).

Q: 2- Use Gauss's divergence theorem to evaluate the surface integral / ry dydz + 2y°dxdz + y?zdxdy),…

A:

Q: Verify the Divergence theorem for the following surface integral A’. dŠ where A (x,y,z) = x²z³i+…

A:

Q: Let i = (a° cos z, 5 – 3a'y cos z – 3yz? sin æ, 2° sin æ) be the velocity field of a fluid. Compute…

A:

Q: 4) Evaluate the surface integral [[F•dS where F(x,y,z)= (yz,-xz,z)and S is the piece of the…

A:

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F= zi+…

A: Calculate the flux of the curl of the field F = z i + 5 x j + y k, by using the surface integral in…

Q: Use the divergence theorem to evaluate the surface integral F · dS, S where the vector field is F =…

A:

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

A: Given ,                                                                             F(x,y) =…

Q: Let v = (5, y sin z, cos z) be the velocity field of a fluid. Compute the flux of v across the…

A: Given, v→=5,y sinz, cosz Flux=∫∫Sv⇀.ds we have divergence theorem, ∫∫Sv⇀.ds=∫∫∫Sdiv v⇀.dv div…

Q: Let E be the solid region bounded by the upper half-sphere x2 + y² + z² = 4 and the plane z = 0. Use…

A:

Q: Evaluate the surface integal [[Curl F.ñ dS for the Sur face and F=xt-y²+ (x+4+z)Ñ and C is the bo…

A:

Q: 3. Use the surface integral is Stokes' Theorem to calculate the flux of the curl of the field F…

A:

Q: Use Stokes' Theorem to evaluate curl F. dS. F(x, y, z) = x2y3zi + sin(xyz)j + xyzk, S is the part of…

A: Stokes theorem: ∫∫ScurlF.dS=∫CF.dr

Q: Let ƒ(x, y, z) = (x2 + y2 + z2)^(-1/2). Show that the clockwise circulation of the field F = ∇ƒ…

A:

Q: Evaluate the flux integral ff. curl (z cos x i+yj+x sin y k) ds where S is the part of the outward…

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Q: 9) Use Stokes' Theorem to evaluate || curl (F)· dS where F(x, y, z) = (x sin z)i+(x)j+(xy)k and S is…

A:

Q: Use Stokes' Theorem to evaluate curl F · dS. F(x, y, z) = x2y3zi + sin(xyz)j + xyzk, S is the part…

A:

Q: Calculate the curl and divergence of F(x, y, z) = x² sin yz i+ z cosxz j+ ye5y k at point (0, 1, 2).

A:

Q: Let S be the surface in R' that is the part of the ellipsoid 2x2 + y² + z? = 2 satisfying y > 1.…

A: In this question, we use the div.  theorem to evaluate the surface integral. given that…

Q: Use Stokes theorem to evaluate ff.curl F.nds. where F = (xyz, x, e* cos z), while S is surface x² +…

A: Solution :

Q: . Evaluate the flux integral f. curl (z cos xi+ yj+ x sin y k) dS where S is the part of the outward…

A:

Q: 4. Evaluate the surface integral ff. F.dS by the divergence theorem where F = (3xy2, yx? -…

A: S is the surface x2+y2≤25, 0≤z≤2 So surface S is a cylinder with radius 5 as shown in below figure.…

Q: #7. Use the Divergence Theorem to calculate the surface integral F dS, S that is, calculate the flux…

A:

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F= 3yi +…

A: Given, F→=3yi^+5-3xj^+z2-2k^r→=3sinφcosθi^+3sinφsinθj^+3cosφk^ So, the flux of curl F is, Flux of…

Q: 3- Use Stokes theorem to compute the line integral ScF - dr, where F = [e-3,e²,e-2=] and C is the…

A: as per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: (4) Use Stokes' Theorem to calculate the work-done by the force field F(r, y, z) = (x² + z²)î + (y²…

A:

Q: 4. A) Find the work done by the force F (x, y) = yx²i – y²j over the curve r (t) = t’i+t*j, 0<t<1.…

A:

Q: Consider the surface S given by y=8−x2−z2, y≥0 oriented in the positive direction of the y axis. be…

A: We will find out the required value.

Q: 1. Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around…

A: We can solve this using Stoke theorem