Verify Stokes' Theorem if o is the portion of the sphere x + y +z² =1 for which z20 and F(x, y,z)=(2x- y)i– yz²j-y°zk .

Q: Let D be the solid in space lying beneath the ry-plane and between the sphere r2 + y? + z² = 3 and…

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Q: Use stokes theorem to evaluate f.dr where f = (4z+y, 3x, 7y) and C is the curve of intersection of…

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Q: Use Stoke’s Theorem to evaluate the line integral ∮C(y+2z)dx +(x+2z)dy +(x+2y)dz, where C is the…

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Q: Use Stokes's Theorem to evaluate f.7 X F.dŠ, where F (x, y, z) = (y +29)î – xj + x³yk and S is the…

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Q: 1. Verify Stokes' Theorem for F = (2x - y)i - yz²j - y² zk, where S is the upper half surface of the…

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Q: Integrate H(x, y, z) = yz, over the part of the sphere x2 + y2 + z2 = 4 that lies above the cone z =…

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Q: Apply Stoke's theorem to calculate S. (x + y – 4)dx + (2x – z)dy + (y + z)dz, where C is the…

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Q: Find a parametric representation for the part of the cylinder y2 + z² = 36 that lies between the…

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Q: Find the equation of the sphere of radius 8 centered at (1, 3, 6). O x² + y² +z² = 46 O x² + y² + z²…

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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: 9. Use Stokes' Theorem to evaluate F. dr where F(z, y, 2) = (2 – y) i + (x + 2)j – (x + y) k and C…

A: The given problem is to evalute the contour integral using stokes theorem, where surface C is the…

Q: Calculate F- dS where F = (3zy', ze", z) S is the surface of the solid bounded by the cylinder y? +…

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Q: (4) Use Stokes' Theorem to evaluate 11. Vx (yz, xz, xy) dS where S is the surface S that is the part…

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Q: Find the centroid of the portion of the sphere x2 + y2 + z2 = a2 that lies in the first octant.

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Q: 2)Use Stokes' Theorem to evaluate [F.dr where E2xyi, y² j‡ 2xzk and Sis the first octant с surface…

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

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

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Q: (a) Between 1 and the disk x²+ (1+x² +y*) (b) Between % = 1 and the entire xy-plane. (1+x* + y?)*

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Q: 2. Use Stokes' Theorem to evaluate , Vx F ·n dS where F(x, y, z) = and C is the part of the sphere…

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Q: 1. The part of the sphere x? + y² + z² = a² that lies within the cylinder x² + y² : = ax and above…

A: To Determine :-  The part of the sphere x2 + y2 + z2 = a2 that lies within the cylinder x2 + y2 = ax…

Q: Use spherical coordinates. Evaluate z dv, where E lies between the spheres x2 + y2 + z² = 1 and x2 +…

A: Using spherical  coordinate we can solve it very easily.

Q: Show that the tangent plane to the quadric surface at the point (x0, y0, z0) can be written in the…

A: Given surface is x2a2+y2b2+z2c2=1 To find the equation of the plane, find the normal of the given…

Q: Consider the parametric surface S given by the portion of the sphere x +y² +z² = 4 where z 2 1.

A: In this question, we have to parameterize the surface in cartesian coordinates and then find the…

Q: Find the extreme values of ƒ(x, y, z) = x2yz + 1 on the intersection of the plane z = 1 with the…

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Q: 4) Use Stokes theorem to evaluate SF.dr, where с F(x, y, z) = <.xy, yz, *x), where C is the triangle…

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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: Write down a parametrization r(u, v) for the portion of the plane x - y+ z = 3 that lies inside the…

A: r(u, v) = ( u cos v , u sin v,  3 - u cos v + u sin v)  Where u € [0, 1]           v€ [ 0,2π]

Q: Calculate the positive value of m so that the x+y+2z=m plane is tangent to the spherical surface…

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Q: 14. Under the paraboloid z=x² +y2 and above the disk x +y² <9 for (x,y) in the first quadrant.

A: we have to find the volume

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…

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Q: Use Stokes' theorem to evaluate $ (xy – y) i – In z j+ (x +x²) k) • dr, where C is the intersection…

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Q: 5. Use Stokes theorem to evaluate J[V x F-ds over the surface of the paraboloid z = 5-x² - y² above…

A: If S  be   smooth surface bounded by a  closed , positively  oriented  smooth boundary curve C with…

Q: Find the average height of the hemispherical surface z = √(a2 - x2 - y2) above the disk x2 + y2 ≤ a2…

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Q: Find %3D as if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = 4-x-y lying above…

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Q: Verify Stokes' Theorum for F(x,y,z) = (y,-x,yz) if S is the paraboloid z = x2 + y2 with x2 + y2 = 1,…

A: Given  Fx,y,z=y,-x,yz Then, F→=yi^-xj^+yzk^

Q: 6. Compute the flux of F = [0, 0, z²] through the spherical surface S given as the upper hemisphere…

A: To find- Compute the flux of F→ = 0, 0, z2 through the spherical surface S given as the upper…

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

A: GivenF(x,y)=x32-8yi+5x+8yj,C: Boundary of a triangle with vertices (0,0), (5,0) and (0,5)To…

Q: Calculate dS where F = (e* sin y, e" cos y, yz²) and S is the surface of the box bounded by the…

A: We need to find the surface integral. We will need basic knowledge of parametrization of vector…

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

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Q: The part of the sphere x^2+y^2+z^2=4z that lies inside the paraboloid z=x^2+y^2

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Q: Plot the implicitly given surface (x − 1)² /4 + (y − 1)² +z² = 1 (a) using the sphere function. (b)…

A: As per the question we have to plot the following surface : (x-1)2/4 + (y-1)2 + z2 = 1 With the help…

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

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Q: Integrate G(x, y, z) = x2y2 + 4 over the surface cut from the parabolic cylinder y2 + 4z = 16 by the…

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Q: Use Stokes' theorem to calculate (V × A) · ndS with A = 3yi – xzj+ yz²k, where S is the surface of…

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Q: Calculate the flux of F across G. F(x, y, z) = 2xi + 2yj + 2zk; G is the surface of the sphere x2 +…

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Q: verify Stokes § = (a%-y)i - yz'i over the uppea hazf SOD Face Of the sphere =1 bounded by the

A: Given that,  F→=(2x-y)i→-yz2j→-y2zk→ To verify Stoke's theorem: ∫CF→·dr→=∬Scurl F→·n^dS Here C is…

Q: (a) The part of the surface z = 1+ 3x + 2y² that lies above the triangle with vertices (0,0), (0,…

A: a) Given part of surface is  z=1+3x+2y2, which lies above the triangle with vertices (0, 0), (0, 1),…

Q: Use Stokes' Theorem to evaluate , (x + y )dx + (2x – 3)dy + (y + z)dz over the boundary of the…

A: First we will learn about Stokes theorem little bit. If "F1 i + F2 j + F3 k" is a differentiable…

Q: 2)Use Stokes' Theorem to evaluate | F.dr where F =2xyi- yj+2xzk and S is the first octant surface of…

A: The given problem is to evaluate the line integral in the surface of first octant with upward…

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: