Stokes' Theorem to evaluate F dr where C is oriented counterclockwise as viewed from Jc F(x, y, z) = i + (x + yz)j + (xy – Vz)k, C is the boundary of the part of the plane 7x + 6y + z = 1 in the first octant.

Q: Use Stokes' Theorem to evaluate o F· dr. F(x, y, z) = xyi + yzj+ zæk where C is the triangle in the…

A: Given that C is the tringle with the vertices (9,0,0), (0, 9, 0) and (0, 0, 9). now choose the…

Q: Question: Verify Green's theorem in the plane for (x³ − x²y)dx + xy²dy, where C is the - C boundary…

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Q: Use Stokes’ Theorem to evaluate ∫ F*dr where C is oriented counter-clockwise as viewed from above.…

A: The vector field is given by: Fx,y,z=yi-zj+x2k The triangle C has vertices 1,0,0,0,1,0 and 0,0,1.…

Q: e Divergence Theorem to evaluate F. dS, where (2x + ey%)i + (y³ + x°z')j+(3y²z)k, and S is the…

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Q: 2. Verify Stokes's Theorem for F(x, y, z) = y i+ z j +x k and the plane x + y + z = 2 in the first…

A: Given, Fx,y,z=yi^+zj^+xk^x+y+z=2 So, curl F is calculating by, Curl F→=∇→×F→Curl…

Q: Directly evaluate the surface integral F(x,y,z)=xyi+yzj+zxk And s is the part of paraboloid that…

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Q: 13. Evaluate . F-di ; where F(x, y, z) = (1,x+ yz, xy – VE) and C is the boundary part of the plane…

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Q: 16. Let F(x, y, z) = xyi+rzj+yzk and C be the curve of intersection between the sphere z² + y° + z²…

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Q: Use Stokes' Theorem to evaluatef fs curl F dS where F(x,y,z) = %3D and S is the portion of the…

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Q: Find the flux of F across the surface σ by expressing σ parametrically. F(x,y,z)= 3i −7j+zk; σ is…

A: The flux of the vector field                           Fx, y, z=xi+yj+zk…

Q: F(x, y, z) = 3yi + 2zj – xk; C is the triangle with vertices %3D (1, 0, 0), (0, 1, 0), and (0, 0,…

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Q: z'y+ y°x +(z+y)x? =1 yüzeyinin P(2, - 1,1) noktasındaki teğet düzleminin denklemi aşağıdakilerden…

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Q: b) the region B in the first octant bounded by the surfaces z =r and r2 +y² + 2 = 1, and c) the…

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Q: The base of the closed cubelike surface shown here is the unit square in the xy-plane. The four…

A: Checking the gradient of the function: Thus, the net outward flux should be 0, The sum of flux…

Q: A surface has an equation of z² + 2x² + 3y² = 4. Through Stoke's Theorem, evaluate the surface…

A: Given: The given equation of surface is z2+2x2+3y2=4. To Find: The surface integral on the upper…

Q: Question No.1: Use Stokes's theorem to evaluate F.Tds where C is the boundary of the part of the…

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Q: 1. Find a number a so that the change of coordinates s =r+ ay,t = y transforms the integral SR drdy…

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Q: The surface S is the part of the paraboloid z = 12 – x² – y² that lies above the plane z = oriented…

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Q: Use a parameterization to find the flux F•n do of F = zʻi+ xj - 2zk in the outward direction (normal…

A: Given : A Parabolic cylinder z = 1 - y² by the planes x = 0, x = 1, and z = 0

Q: Evaluate the surface integral / - 2a dS. Where S is the triangular region with vertices (5,0,0), (0,…

A: Here is the solution of the given problem.

Q: 7. Use Stokes' Theorem to evaluate f, F· dr where C is oriented counter- clockwise as viewed from…

A: Given Fx,y,z=yi-zj+x2kC is the triangle with vertices 1,0,0, 0,1,0, 0,0,1and the triangle is a…

Q: 4. Use Stokes' Theorem to evaluate [ F• dr when z = 4-y F(x, y. 2)= xz° 7+(x+z*)7+ -x |k. Let C is…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Use Stokes's Theorem to evaluate JCF•dr. Use a computer algebra system to verify your results. C is…

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Q: 2. A surface S in R'(r,y, :) is defined parametrically in the form 2u 2r u? + v² - 1 X(u, e) = (I+…

A: For a surface X(u,v) cross product of Xu(u,v)  and Xv(u,v) gives normal vector to tangent plane…

Q: 25-28. Surface integrals using a parametric description Evaluate the surface integral s f dS using a…

A: surface integral of the surface that is parameterized as…

Q: 22. A surface has an equation of z² + 2x² + 3y² = 4. Through Stoke's Theorem, evaluate the surface…

A: Given : F=xi+yj+x+y2k             z2+2x2+3y2=4 To Find : Surface integral

Q: Using Stokes’ Theorem to evaluate a line integral Evaluate the lineintegral ∮C F ⋅ dr, where F = z i…

A: Given Data The function is F=<z,-z,x²-y²>. The equation of the plane is z=8-4x-2y. The limits…

Q: Use a parameterization to find the flux The flux is SSF n da of F = 2²1+xj-32k in the outward…

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

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Q: Using Stokes's theorem, calculate the line integral is the triangle with vertices (0,0,0), (1,0,0),…

A: To use Stokes's theorem to calculate the line integral of the below function. F=2y2, 3x2, z−x The C…

Q: Use Stokes' theorem to evaluate dr. Assume C is oriented counterclockwise as viewed from above. F=…

A: To use the Stokes' theorem to evaluate the line integral.

Q: Evaluate the surface integral I. -4x dS. S Where S is the triangular region with vertices (4, 0, 0),…

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Q: Let S be the portion of the plane z = 7x contained in the half-cylinder of radius R = 3 depicted in…

A: According to the given information, it is required to use the stokes theorem to find the circulation…

Q: A surface has an equation of z² + 2x² + 3y² = 4. Through Stoke's Theorem, evaluate the surface…

A: A surface has an equation of z2+2x2+3y2=4 To evaluate the surface integral on the upper half of the…

Q: triple integral /// y dV; G is the solid enclosed by the Evaluate the plane z = y, the xy-plane, and…

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Q: Verify Stokes' theorem on a region which is a portion of the sphere r+y+2= 16 which lies above the…

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Q: c) Use Stokes's theorem to evaluate o F. dr, where F(x, y, z) = xy² i+x°yj+ yz k, %3D where C is a…

A: Given, Fx,y,z=xy2i^+x2yj^+yzk^ Now, ∫CF→.dr→=∫∫Scurl F→.dS→

Q: F(x, y,z) = (2xz) i+(1-4xy“) j+(2z-z) k and S is the surface of the solid bounded E z6%- 2x2 – 2y²…

A: Given function is: F=2xzi+1−4xy2j+2z−z2k Here S is the surface of solid bounded by the below…

Q: A surface has an equation of z² + 2x² + 3y² = 4. Through Stoke's Theorem, evaluate the surface…

A: Given: The surface's equation is z2+2x2+3y2=4. To find: The surface integral on the upper region of…

Q: 5. Test the Stokes' theorem for the function: V 3xy'x-zcos (2x)ÿ + xy°ż .Do it for the plane surface…

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Q: Verify stokes theorem for F = (2x- y)i – yz'j - y zk over %3D the upper half surface of the sphere…

A: Given the field, F¯=2x-yi¯-yz2j¯-y2zk¯ S is the upper half surface of the sphere x2+y2+z2=1 bounded…

Q: Let D be the solid region in space bounded above by z = 6 – x² – y², below by z = 0, and laterally…

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Q: find a parametrization of the surface. 1.The portion of the cylinder x2 + z2 = 4 above the xy-plane…

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Q: Stokes’ Theorem on closed surfaces Prove that if F satisfies theconditions of Stokes’ Theorem, then…

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Q: II3. S is the part of the paraboloid z = x² +y² below the plane z = 4 oriented upward and F(x, y, z)…

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Q: Given F(x,y,z) = < 3xz, yz, xz > and C is the boundary of the portion of the plane x + 2y + z…

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Q: Set up and simplify the surface integral ∬S F dS where F(x,y,z) = 2xi + yzj - √y k and S is the part…

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Q: Evaluate  ∫s∫curl F * N dS (dot product)  where S is the closed surface bounded by the graphs of x…

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Q: What is the center of gravity of the solid formed when the plane region bounded by 2x+y-2= 0, y = 0…

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