Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. F = yi+xzj+x²k C: The boundary of the triangle cut from the plane 9x + y + z = 9 by the first octant, counterclockwise when viewed from above. The circulation is (Type an integer or a fraction.)

Q: In Exercises use the surface integral in Stokes' Theorem to calculate the circulation of the field F…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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

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

Q: F= (y, 2x, -z) and C is the circle x² +y² = 9

A:

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: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = (y +z*)i+…

A:

Q: 14. Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field: F =…

A:

Q: use the curl integral in Stokes’ Theorem to find the circulation of the field F around the curve C…

A:

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

A:

Q: Find the counterclockwise circulation and outward flux of the field F = xyi + 4yʻj around and over…

A:

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: Which of the following is the circulation of the field F in the direction indicated on the curve C,…

A:

Q: find the circulation and flux of the field F aroundand across the closed semicircular path that…

A:

Q: Find the line integral of the field F = over the portion of the ellipse * + y = 1 lying in the first…

A:

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = +z)i+ (x…

A:

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

A:

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

A:

Q: use the surface integral in Stokes’ Theorem tocalculate the flux of the curl of the field F across…

A: Given  F=(y-z)i+(z-x)j+(x+z)k S:r(r,θ)=(rcosθ)i+(rsinθ)j+(9-r2)k 0≤r≤3, o≤θ≤2π

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: find the circulation and flux of the field F aroundand across the closed semicircular path that…

A: The given vector field is Fx,y=-yi+xj.

Q: Use Stokes' Theorem to calculate the work done by the field F through the shell S. F = x 4i + 7x j…

A:

Q: Use the Stokes' Theorem to caleulate the circulation of the field F = -6y*7 + 6x*J° + 7z*R° around…

A: Given field, F→=-6y3i^+6x3j^+7z3k^ where C is the curve of the paraboloid x2+y2=z cut by the…

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

A:

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

A: Given The given vector field is F=yi+xzj+x2k and the surface is 8x+y+z=8. Apply formula…

Q: ) Verify Stokes' Theorem for the hemisphere S : x²+y²+z² = 9, z > 0, %3D its bounding circle C: 1?…

A: Stokes theorem  If a smooth surface S bounded by closed ,smooth boundary curve C oriented in…

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F= 2zi +…

A:

Q: Find the flux of the field F = x i + y j + z k outward through the portion of the cylinder x2 + y2 =…

A:

Q: 4. Verify Stokes's Theorem for the vector field F(x, y, z) = ( yz, – xz, z) over the cone z² = x² +…

A: a) Given that the vector field Fx,y,z=yz,-xz,z over the cone  z2=x2+y2 with 0≤z≤2 oriented downward.…

Q: Use the surface integral in Stokes' Theorem to calculate the rotation of the field F = (y? + z?)i +…

A:

Q: 14. Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field: (r…

A:

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

A:

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

A:

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

A:

Q: use the surface integral in Stokes’ Theorem tocalculate the flux of the curl of the field F across…

A:

Q: Use Stokes' Theorem to find the value of the line integral of the vector field F around the curve C…

A:

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 2zi +…

A:

Q: Use Green's theorem to find the counterclockwise circulation and outward flux for the field F =…

A: F=(y3-ey sinx) i + (y3+ey cos x) jr2=sin(2θ) we have to calculate the counterclockwise circulation…

Q: 18. F = 1 + i + (tan' y)j x² + y? = 1

A:

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

A: By  stoke's theorem ∫∫sCurl F.dS  =∫∂sF.ds

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

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: Calculate the circulation of the field F around the closed curve C. Circulation means line integral…

A:

Q: Apply Green’s theorem to find the outward flux for the field F =tan^−1?(y?/x)i+ln(x^2+y^2)j and…

A:

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = x²i+…

A: Given : F=x2i+4xj+z2k

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = (y +z)i+…

A:

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

A: Here, the given vector field is: F=x2i+5xj+z2k⇒curl F=ijk∂∂x∂∂y∂∂zx25xz2…

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = by the…

A:

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

A:

Q: use the curl integral in Stokes’ Theorem to find the circulation of the field F around the curve C…

A:

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

A: Given field : F=x2yi+2y3zj+3zk    surface S is r(r,θ)=(r cosθ)i+(r sinθ)j+rk    0≤r≤1,     0≤θ≤2π

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F =xi+ 5xj +zk…

A: