Use Stokes' Theorem to evaluate F. dr where F(x, y, 2)æzî + 2ry} +3ryk where C is the boundary of the part of the plane 3x + y + z = 3 in the first octant and C is oriented counterclockwise as viewed from above.

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

A:

Q: 11. Use Stokes' Theorem to evaluate OF dr where F=(xz,e",y+z) on the curve that is the intersection…

A: The equation of curl is F=xz,ey,y+z. The equation of plane is 6x+3y+z=12

Q: Evaluate the surface integral. xz ds, S is the part of the plane 2x + 2y + z = 4 that lies in the…

A:

Q: Use Stokes theorem to evaulate ⌠c F*dr where F(x,y,z)=2i+yj-xk and C is the boundary of the part of…

A: F(x,y,z)=2i+yj-xk C: z=9-x^2-y^2  z=0

Q: Use Stoke's theorem to evaluate the integral xydx +2x 'dy-&r 'zdz where C is the boundary of the…

A:

Q: Evaluate the surface integral xyzdS where S is the part of the plane z = 1 + 2x + 3y that lies above…

A:

Q: Integrate G(x, y, z) = y + z over the surface of the wedge in the first octant bounded by the…

A:

Q: Find the area of the plane xtay-zt 10=0 that lies above the disk xy-plare

A: Given that, Area of plane is x+2y-z+10=0 It lies above the disk {(x,y)/x2+y2≤4} in x,y plane. The…

Q: Use the Divergence Theorem to evaluate the surface integral (2x^2 + 3yz + 4xz) dS where S is the…

A:

Q: Evaluate the surface integral. /| xz ds, S is the part of the plane 2x + 2y + z= 4 that lies in the…

A: We need to find surface integral.

Q: Evaluate the surface integral: x dS,  S is the part of the plane  12x + 6y + z = 12  that lies in…

A: From the given statement, the plane is 12x + 6y + z = 12 and it is lies in the first octant.

Q: Use Stokes' Theorem to evaluate F. dr where F(x, y, z) = xi + yj +Xx² + y² )k and C is the boundary…

A: Stokes theorem: ∮f→·dr→=∬S curl f→·n^ ds Given F(x, y, z)=xi + yj+9(x2+y2)k and C is the boundary of…

Q: Use Stokes' Theorem to evaluate | F - dr, where F (x, y, z) = zi + yj – xk and C is the 9 – z? y? in…

A: Given F→x,y,z=zi^+yj^−xk^ We have to evaluate ∫CF→⋅dr→,where C is the boundary of the part of the…

Q: Use Stokes' Theorem to evaluate SSs curlF · dS, where F(x, y, z) = 7xyi + 3yzj+4z²k and S is the…

A: Consider the provided question, Use Stokes' Theorem to evaluate ∫∫Scurl F·dS,where F(x, y, z)…

Q: (b) Verify Stokes' theorem on a region which is a portion of the sphere x? +y? +z² = 16 which lies…

A:

Q: b) Use Gauss theorem to evaluate F.ndS, where F(r, y, 2) = (2x²y² + In z) i – xy³ j – tanh(a² + y³)…

A:

Q: Use Stokes' Theorem to find the line integral of F = 3yi + 2zj + 5xk around a 5, oriented…

A: The solution are next step

Q: (b) Verify Stokes' theorem on a region which is a portion of the sphere r2 +y² +2 16 which lies…

A:

Q: Use Stokes' Theorem to evaluate F. dr where C is oriented counterclockwise as viewed from above.…

A:

Q: Integrate G(x, y, z) = xyz over the surface of the rectangular solid cut from the first octant by…

A: Given: G(x,y,z)=xyz We have to integrate G(x,y,z) over the surface of the rectangular solidcut from…

Q: Find the area of the surface of the part of the plane 3x + 2y + z = 6 that lies in the first octant.

A:

Q: Use Stokes' Theorem to evaluate of intersection of the plane x + 3y +z = 12 with the coordinate…

A:

Q: Use Štoke's Theorem to evaluate the line integral - 2ydx +-6zdy + dz where C is the intersect | of…

A: Strokes theorem is ∫CF→.dr→=∫∫S∇×F→.N→dS=∫∫ScurlF→.N→dS x=rcosφy=rsinφ

Q: Use Stokes' Theorem to evaluate the line integral (y + 2z)dr + (x + 2z)dy + (x+ 2y)dz where C is the…

A: Given intgeral. ∫Cy+2zdx+x+2zdy+x+2ydz The Curve is formed by the intersection of the sphere…

Q: Use Stokes's Theorem to evaluate f. F dř where F(x, y, z) = (x- y) i+ (y-z)j+ (z - x) k and S is the…

A:

Q: Verify Stokes' Theorem if F(x, y, z) = (x – y)i + (y – z)j+ (z – x)k and S be the portion of the…

A: Solution: The objective is to verify the Stokes theorem for the given problem

Q: Use Stokes' Theorem to evaluate [[(curlF)•ndS where F(x,y,z) =x’i+z°j-y°k and o is that portion of…

A:

Q: Find the area of the surface cut from the paraboloid x2 + y2 - z = 0 by the plane z = 2.

A:

Q: Use Stokes’ Theorem to evaluate the line integral  ∮  F·d r where F = 〈x^2−z^2, y, 2xz〉, and C is…

A:

Q: Integrate G(x, y, z) = xyz over the surface of the rectangular solid bounded by the planes x = ≠a, y…

A: When we consider the face we find Using the formula of we have

Q: Use Stokes' Theorem to evaluate F. dr where C is oriented counterclockwise as viewed from above.…

A: Given that  Fx,y,z=i+x+yzj+xy-zk and C is the boundary of the part of the plane 5x+4y+z=1 in the…

Q: Use Stokes' Theorem evaluate 4F.dr if to F(x, y,z)= xzi+ xyj+3xzk and C is the boundary of the…

A:

Q: Integrate g(x,y,z) = x + 5y + z over the portion of the plane 4x + 8y + z = 8 that lies in the first…

A:

Q: Find the surface area of the plane 3x + 2 y + z = 6 that lies in the first octant.

A: The surface area of the plane z=f(x,y) is given by the formula                          S=∬D…

Q: Find the area of the part of the plane defined by 3z + 2y + z 12 that lies in the first octant.

A: Given equation of plane :  3x+2y+z= 12

Q: Use Stokes' Theorem to evaluate  F · dr  where C is oriented counterclockwise as viewed from above.…

A:

Q: b) Use Stokes' Theorem to evaluate fF•dr for F(x,y,z) =-yi+ xz j+ zk where C is the curve of…

A:

Q: Find the area of the surface. The part of the plane 3x + 5y + z = 15 that lies in the first octant

A: Given plane,  3x+5y+z=15Intercepts of the plane axis are  x=5, y=3, z=15

Q: #6. Use Stokes' Theorem to evaluate S. F dr, where F(x, y,2) = i+(x + yz)j+(xy-V) k and C is the…

A: Given that, Fx,y,z=i+x+yzj+xy-zk and C is the boundary of the part of the plane 3x+2y+z=1 in the…

Q: Use Stokes' theorem to calculate , F.ds, where F = (z, x, y) and C is the boundary %3D of a triangle…

A:

Q: The surface area of the part of the paraboloid z=x+y that lies under the plane z=2 is: Z=,

A: Surface area is given as A=∬D1+δzδx2+δzδy2dA

Q: Use Stokes theorem to evaluate F- dr. where F = (2, 2z, y) and C is the boundary of the paraboloid…

A: Stokes theorem: ∫CF.dr =∫∫Scurl F.N ds Curl F of the vector function F=f1i+f2j+f3k is…

Q: Evaluate the surface integral. SS, xz ds, S is the part of the plane 2x + 2y + z = 4 which is in the…

A:

Q: Use Stokes' Theorem to evaluate F. dr where C is oriented counterclockwise as viewed from above.…

A: Stokes's theorem ∬ScurlF.dS=∫CF.dr where, C is the boundary of the surface oriented…

Q: Verify Stoke's theorem for F = -2yzi + vj +3xk over the surface defined z = 5- x² -y? above the z=1…

A:

Q: Cvaluate AP G is a solid in the first octant bounded by the plane y+ z = 2 and the urface y = 1 -…

A:

Q: Integrate G(x, y, z) = x + y + z over the surface of the cube cut from the first octant by the…

A: Definition used:

Q: Find the surface area of part of the paraboloid z = f(x, y) = x^2 + y^2 that lies under the plane z…

A:

Q: Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant. (Use…

A: Part of the plane equation   5x+4y+z=20⇒z=20-5x-4yPlane lies in the first octant , so x≥0 ,…