Let F(x.y.z)=-y²i+xj+z² k, S is the shaded part in the figure at right and C the boundary curve of S x² = 16– 4z x – 4y + z = 4 y 3 | a) Calculate www ww F.d using stokes theorem

Q: Let F(x, y, z) = (-y, xy, 0) and C be the curve of the intersection of z = x² + y² and z = 2x such…

A: Given clear answer below

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

A: Here, F=<exsiny,excosy,yz2>

Q: Let F(x, y, z) = 2yzi+ 4.xzj+ e*yk, and let C be the circle x2 + y² = 16, z = 3, oriented…

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Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

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Q: 2. Let F = −y³i + x³j + cos z³k and C be the curve generated by the intersection of the cylinder x²…

A: a. Given, F¯=-y3i¯+x3j¯+cos z3 k¯ Let C be the curve generated by the intersection of the cylinder…

Q: 6. Let S be the sphere 2 + y² + z² = 1 and F(x, y, z) = (x + e*+y, y+ In(sin(z)), z). Calculate the…

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Q: The region W lies between the spheres x2+y2+z2=1 and x2+y2+z2=9 and within the cone z=x2+y2−−−−−−√…

A: Given: The region W lies between the spheres       x2 + y2 + z2 = 1 and x2 + y2 + z2 =9 with in the…

Q: Find the circulation of F(x, y, z) = (-y sin 2, x sin z, xy cosz +12) around the circle cut from the…

A: Given that,F(x, y, z)=(-ysinz, xsinz, xycosz+12) around the circle cut from the sphere x2+y2+z2=5 by…

Q: Let F = (-z, x, y²). Find curi Fds, where S is the paraboloid z = x2 + y?, 0 < z< 4. (You can do the…

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

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Q: Use Stokes' Theorem to find the line integral of F = (xy, yz, xz) around the boundary of the surface…

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Q: I = y dx + (z — х) dy — ydz, Jc

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Q: EXERCISES 2.10 1. Use Stokes' Theorem to evaluate E.dr for F=(xz,-y,x²y), where C is the boundary of…

A: Given: F=&lt;xz,-y,x2y&gt; C surface, S is bounded by x=0, y=0 and 2 not include xy-plane Now,…

Q: 3.) Verify the conclusion of Stokes' Theorem given F(x,y,z)=(x-y,y-z,z–x) where S is the surface cut…

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Q: Verify Stokes' Theorem for F(x, y,z)= (y,-x, yz) and S is the paraboloid z = x² + y° , 0<zsl. Assume…

A: ∫F→.dr→=∫∫Scurl F.n dA.Here  Fx,y,z=y1-x1 yzS  is the parabloid  Z=x2+y2, 0≤Z≤1

Q: 2). Find the flux of F(x, y, z) = (0, yz, z) outward through the surface S cut from the cylinder y +…

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Q: Use Stokes' Theorem to find the line integral [((x² + 2y² ((x + 2y²)i + (y + 2²)j + (2 + 2x²)k) · dř…

A: Given that C is boundary of triangle with vertices 1,0,0,0,1,0,0,0,1 So, equation of the plane with…

Q: 3- Use Stokes theorem to compute the line integral F . dr, where F = [e-3y, e, e201 and C is the…

A: By using the stokes theorem we need to find ∫CF·dr, where F=e-3y, ez, e-2x and C is the boundary of…

Q: d) An open surface F is given by F = {(x,y, z) |z = 4 – x² – y² , z > 0} . Compute the flux of V…

A: V(x,y,z) = &lt;2x+3y,2y+3x,-4z&gt;F={ (x,y,z) : z=4-x2-y2 , z≥0}Consider, g(x,y,z) = z+x2+y2-4…

Q: Use Stokes' Theorem to find the line integral [((x² + x + 2y²)i + (y + z³)j + (z + 2x²)k) · dr where…

A: To Evaluate: The integral ∫C(x+2y2)i+(y+z2)j+(z+2x2)k·dr. where C is the boundary of the triangle T…

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 the circulation line integral ∫_c F·dr where         F(x, y, z) =…

A: Given vector field is Fx,y,z=z2-x+x2-yj+y2-zk Then,  ∇×F=ijk∂∂x∂∂y∂∂zz2-xx2-yy2-z=2y,2z,2x Given…

Q: Let C be the curve intersection of the sphere x'+y+=9 and the cylinderx+y° =5 above the xy-plane,…

A: To Evaluate: ∫CF·dr Using Stoke's theorem. where F→=&lt;2yz,5xz,lnz&gt; and C is the curve of the…

Q: EXERCISES 2.10 1. Use Stokes' Theorem to evaluate F.dr for E = (xz,-y,x²y), where C is the boundary…

A: Applying stokes theorem we solve it

Q: Consider the surface F(x, y, z) = x°z³ + sin(y+z5) – 7 = 0. Find the following partial derivatives…

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Q: Use Green's Theorem to evaluate the line integral S(x² + y²)dx + (x² – y²) dy where C is the…

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Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

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Q: Set up the surface integral for upward Flux of the upper hemisphere of radius = 5 (z20) such…

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Q: Use Stokes' Theorem to evaluate fF.dr if F(x,y,z) =( z-y)i +(x+z)]- (x +y)K and C is the curve of…

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Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

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Q: Let F = −y³i + x³j + cos z³k and C be the curve generated by the intersection of the cylinder z² +…

A: As per the question we are given a vector field F(x,y,z) and a curve C defined as the intersection…

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. y10 dx + x6…

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Q: Let F (x, y, z): = (x + 2y2, y + z2, z + 2x2), and let C be the curve that results from the…

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Q: Evaluate the line integral F. dr where F(x, y, z) = x²y i+ x³ j+e² tan-¹ z k and C is the curve of…

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Q: aluate the line integral fc F dr, where F(x, y, z) =3 sin xi + 2 cos yj+ 4xzk and C is given by the…

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

A: According to the given information, it is required to use the stokes theorem to compute line…

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

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Q: Let S be a square plate with boundary C having length of each side as 2 units, lying in the plane z…

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Q: 2) Find the area of the surface r(u,v)=u cos vi+u sin vj+2vk where 0su<3 and 0<vs 2n .

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Q: Use Stokes's Theorem to show that 0= [[ curl(F) - dS where F(r, Y, z) = (2, 2ry, x + y) and S is the…

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Q: JS S is the surface of the solid bounded by the cylinder x = y² and the planes x + z = 1 and z = 0.…

A: Here we will use divergence theorem to find flux of given vector field across S In  a simple solid…

Q: Let F(x.y.z)=-y²i +xj+z? k, S is the shaded part in the figure at right and C the boundary curve of…

A: We will find out the required value.

Q: Evaluate (x² + y) dv G if G is the solid bounded by the parabolic cylinder z = the planes x = 0, x =…

A: Here I am using simple tripple integration to solve this question.

Q: curl(F) N dS, where F(x, y, 2) = -y(x² + y²)2021 î + In(z +1)e²*y² }+ 22021 vx² + y² k and S is the…

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Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. e5x + 2y dx +…

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Q: Let F = ( ) 5x* + 16z, 2x³ + 3y² + 16z, x + y + eVz³+1 and C be the curve defined by 7(t) = (2…

A: Given that,  F=5x4+16z, 2x3+3y2+16z, x+y+ez3+1 And rt=2cost, 2sint, 16cos2t sin2t, o≤t≤π To find…

Q: Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points…

A: Consider the provided question,

Q: 4. Use Stokes' Theorem to evaluate |F• dr when F(x, y, z)= z' i+y° j+xy k. Let S is the part of the…

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Q: 2. Consider the triangle {(x, y)| x, y > 0, 2x + y < 1}. Let C be the boundary of this triangle…

A: Given triangle is x,y:x,y≥0,2x+y≤1. Let C be the boundary of this triangle oriented in the…

Q: Let C be the curve of intersection of the cylinder x2 + (y- 1)2 = 1 with the plane y = z, traversed…

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