Let F = < 4x + y², 5y + z, 9z + x So F. dī, Use Stokes' Theorem to evaluate C where C is the triangle with vertices (7,0,0), (0,7,0), and (0,0,7), oriented counterclockwise as viewed from above.

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

A: The vector field is Fx, y, z=x+y2i+y+z2j+z+x2k. The equation of the plane is x+y+z=3. Consider…

Q: Use Stokes's Theorem to evaluate Jo F. dr. In this case, C is oriented counterclockwise as viewed…

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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: 4. Use Stokes’ theorem to evaluate fa F. dr, where F(x,y, z) = (xy,yz, zx), and C is the triangle…

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

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

A: Given:     Stokes'Theorem :                            ∫cF·dr =∬scurlF·ds   If F=Pi+Qj+Rk,…

Q: Let z = g(x, y) f2(3, 6) = 5. f(3 cos(ry), y + e=y) provided that f(3,6) = 3, f1(3,6) = 2, i) Find…

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Q: Let z = g(x, y) = f(3 cos(ry), y + e=") provided that f(3, 5) = 5, f1(3, 5) = 2, f2(3, 5) = 4. %3D…

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Q: Let z = g(x, y) = f(3 cos(xy), y+ey) provided that f(3,5) = 3, f1(3,5) = 2, f2(3, 5) = 4. i) Find…

A: In this question we have to find following parts.

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

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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.

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

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

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Q: 3. Use Stokes' Theorem to evaluate $ F dr, where F = (0, 0, 2), (1, 0, 2), (1, 1, 2), and (0, 1, 2),…

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Q: c) Verify Stokes's Theorem for F = (x²+y²)i-2xyj takes around the rectangle bounded by the lines x…

A: Stoke's law is given as ∫cF→.dr→=∫s∫∇×F.n→ds F=x2+y2i^-2xyj^ dr→=(dxi^+dyj^) So F.dr=x2+y2dx-2xydy…

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

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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: Evaluate . F dr where F(x,y,z) = (cos x, -2x, y + sin(z³)) and C is the boundary of the triangle…

A: This is a problem of surface integral.

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: Let F: = . Use Stokes' Theorem to evaluate curlF · dS, where S consists of the top and the four…

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Q: 6. Use Stokes theorem to evaluate $. F•dr, where F = (-3y² , 4z, 6x) and C is the triangle in the…

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · d5, where S consists of the top and the four…

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Q: Use Stokes's theorem to evaluate o F· dr, where F(x, y, 2) = xy² i+x²yj+yz k, where C is a…

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Q: Let F(x,y,2)=(6y,42,6x) a pply stokes' Theorem to eveluate F.dr by finding the flax of ceerl(F)…

A: Given F¯(x, y, z)=6y, 4z, 6x By Stoke's theorem ∮cF.dr=∯s(curl F).n^ds and vertices of triangle are…

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

A: Here use the stokes theorem to find the integral of the function.  And given that the function…

Q: Attached picture is the question

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Q: Use Stokes’ Theorem to evaluate ∫c F ⋅ dr. In each case C is oriented counterclockwise as viewed…

A: Given: f(x,y,z) = xyi + yzj + zxk C is part of paraboloid z= 1- x2-y2   so, A/c to stroke theoram…

Q: S,F•dr, and C is the triangle, with Use Stokes Theorem to evaluate where F(x,y; =) = (x+ y² )i+ (vy+…

A: Given: Fx,y,z=(x+y2)i+y+z2j+z+x2k and C is the triangle with vertices 1,0,0 ,0,1,0 and 0,0,1 We know…

Q: 11. Let F = (-xy + xz²)i + (4xz + y²)j + e² k. Use Stokes' Theorem to calculate fcF. dr, where C is…

A: We have to find∫cF→.dr→.

Q: Q2. Use the Stokes' Theorem to find fF.dr where F(x,y,z) = and C z=9-x²-y² on the xy plane oriented…

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S consists of the top and the four…

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Q: Use Stokes' theorem frotF. ds to evaluate F(x, y, z) = (x + tan¯¹yz)i + y²zj + zk, S is the part of…

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Q: Use Stokes's theorem to evaluate F.dr, where F(r, y, z) = ry i + x°yj+yz k, where C is a triangular…

A: Stroke's theorem:  ∫Fdr=∬ (Curl F) n^dS Curl F=ijkxy2x2yyzy2x2y=iz n^=∇s∥s∥=i^+k^2

Q: Let F = [4z?, x2, 2y²] and C be the positively oriented boundary of the triangle with vertices (0,…

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

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

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Q: Use Stokes' theorem to evaluate V ×F· î dS where = (9y²z, 4xz, 2x²y²) and S is the paraboloid z = x²…

A: Step:-1 Stoke's Theorem:- ∬s∇×F→.n dS=∫F.dr Now, given that F→=9y2z, 4xz, 2x2y2 and paraboloid…

Q: Use Stokes' Theorem to find m # 0 satisfying F · dr = -5, whereF(r,y, z) = (3yx² + z³, y², 4yx²) e C…

A: Given:

Q: Let ~F = (−xy + xz2)~i + (4xz + y2)~j + ez ~k. Use Stokes’ Theorem to calculate ∫C ~F ·d~r, where C…

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

A: Answer is in next step. please give a like!!

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

A: Concept Used: ∫CF·dr=∫∫ScurlF·dS Where C is the boundary of the surface oriented counterclockwise

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's theorem to evaluate F dr, where F(r, y, z) = ry i+x*yj+yz k, where C is a triangular…

A: Given that, F(x,y,z)=xy2i+x2yj+yzk Using the stoke's theorem, ∮F.dr=∬S(curl f.n)dS Now let's find…

Q: Jse Stokes' Theorem to evaluate F. dr where F(x,y, z) = xi + yj+ 2(x² + y²)k and C is the boundary…

A: answer is in next step

Q: Use Stokes's Theorem to evaluate EF. dr. In this case, C is oriented counterclockwise as viewed from…

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Q: Verify Stokes' theorem for F = z²i – y²j and the curve C is the square in the xz-plane from (0,0, 0)…

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

A: The given line integral is ∮CF→·dr→ Where, F→=yzi^+6xzj^+exyk^ C is the circle x2+y2=9 at z=8 The…

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: Use Stokes' Theorem to find the line integral (x+ 2y°)ï+ (y + z²)j+ (z + 2r²)k) · dř where C is the…

A: To find the line integral, Using stokes theorem.

Q: Use Stokes' Theorem to evaluate |/. CurlF dS, where F(r, y, 2) = xyzi + xj + e" cos zk and S is the…

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