5. Test the Stokes' theorem for the function: V 3xy'x-zcos (2x)ÿ + xy°ż .Do it for the plane surface bound by the lines: (0,0,0) => (1,0,0) => (1,1,0) => (0,1,0) =>(0,0,0). zt

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: Find the coordinates of the centroid of the curve given belov x = cos t+tsin t, y =t cos t- sin t,…

A: Given data: The x-coordinate of the curve is x=cos t+tsin t. The y-coordinate of the curve is y=tcos…

Q: Use Stokes' Theorem to evaluate for F. dr. F(x, y, z) = 5xyi + 5yzj + 5zxk C where is the triangle…

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: 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: 1. Evaluate the surface integral fs (r + y + z)dS, S is the parallelogram with parametric equations…

A: We are entitled to solve only one question at a time. As the question number is not mentioned, So we…

Q: Verify Stokes' theorem for F = (x+y-4) i+3xy j+ )k, over the surface of the hemisphere x2 + y2 + z2…

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Q: (5) Use Stokes' Theorem to find the line integral |(* + 2y°)i + (y + z°) +(= + 2r*)k) • dř where C…

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Q: Use Stokes' theorem to evaluate Ĝ - dĩ, vhere Ĝ(1, Y, 2) = (2r, y,0) and D is any closed curve.

A:

Q: 4. Let II be the plane tangent to the implicit surface x²y° + e²= = 5+ 2y sin(z) at the point (-2,…

A:

Q: 3. Use Stokes' theorem to evaluate the line integral F· dr where A = -yi + xj and C is the boundary…

A: Stoke's theorem given by ∫CF.dr=∫∫Scurl A×n^ds According to the question, A=-y i+x j…

Q: Find the polar moment of inertia about the origin of a thin triangular plate of constant density d =…

A:

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: ns: Find the tangent plane to the surface of x2 + z² = y² + 9 at (1, –1,3). 3

A: Follow the procedure given below.

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: Consider the equation yz = 4x² + y² -z Use the Implicit Function Theorem to show that the given…

A: a. Given : equation xyz=4x2+y2-z2 To show : given equation has a local solution about the point 2,…

Q: Calculate F - dS where F = (e² sin y, e² cos y, yz²) S is the surface of the box bounded by the…

A:

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: 18 Verify Stokes' theorem F.dr = (curl F)· dS C S where F = (x² + y – 4, 3xy, 2xz +z?) and S is the…

A: We have

Q: 2/ MATH

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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→=<2yz,5xz,lnz> and C is the curve of the…

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

A:

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

A:

Q: Attached picture is the question

A: Consider the provided question,

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

A:

Q: Evaluate the unoriented line integral (2æ² + y² + z²) ds along the parametric curve a : [0, 1] → R³…

A:

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

A:

Q: .† Use Stokes' theorem to show that Sc(y+2)dx+ (z +x)dy+ (x+y)dz = 0, where C is the curve of…

A:

Q: | 5y? dx +xy dy

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Q: Find the equation of the tangent plane at the point x = xo = 4, y = yo = 1 of the surface %3D z =…

A: Option C is true

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: Find the work done by F in moving a particle once counterclockwise around the given curve = (2x –…

A:

Q: '. Use Stokes' Theorem to compute || CurlF •dS for the hemisphere x + y +z² =9, z20, intersected…

A:

Q: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,27). y = sinx 4 56 1 3. 6…

A: The given equation of the curve is: y=sinx To draw the given equation on the x-y plane we need to…

Q: Let F(x, y, z) = (8 + 8y+ 3z+yz, 6x + 6y + 2z+ cz, 5x + 4y+ 10z+ ry). and let C be the curve that…

A:

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: 11. Consider F(x, y, z) = (-y, x, e²) and the surface defined by S = {(x, y, z) : z =1– 2² – y², x²…

A: Given F=-y,x,ez and S=x,y,z| z=1-x2-y2,x2+y2≤1. Verify the stokes theorem ∫CF·dr→=∬Scurl F·n→ dS.

Q: 4. Let S is the surface z = 5- - y, 1s z in R. Let S be oriented with the normal vector pointing…

A:

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…

A:

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

A:

Q: - S is the surface with parametric equations x = 3u+v, y = 3u-v, z = uv for (u, v) in the region D…

A: We will find out the required value.

Q: 1. Use Stokes' Theorem to evaluate curlF.dS where F =z'i+ (4y-y) j+2zk and S is the portion of z = r…

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Q: Use Stokes' Theorem to evaluate fr. F. dr. C F(x, y, z) = 5xyi + 5yzj + 5zxk where is the triangle…

A:

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: 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: iv) Given F (x, y, z) = -yzį + 2xj + xyzk be a vector function that passes through a surface S of z+…

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Q: Use Stokes' Theorem to calculate fe F-dĩ, where F = zyi+3=j+5zk, and C is the closed path around a…

A: Here given that F→=xy i^+3z j^+5x k^ and curve C in xz-plane. To find: ∫C F→·dr→ by Stokes' theorem.

Q: 3- Use Stokes theorem to compute the line integral SF· dr, where F = [e-3y, e², e-2*] and C is the…

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

A: