Use Stokes' Theorem to find the line integral (x+ 2y°)ï+ (y + z²)j+ (z + 2r²)k) · dř where C is the boundary of the triangle T with vertices (1,0,0), (0, 1,0), (0,0, 1) and oriented counter-clockwise when viewed from above.

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: 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: Evaluate the integral for y dx +z²dy + x²dz, where C is the triangular closed path joining the…

A: Stokes theorem:  Let C be a closed curve S be a surface enclosed by curve C. F is defined every…

Q: Use Stockes' theorem to calculate the line integral f. F dr where x, y, z 3xy + e?va-1 i + ( 2x2 –…

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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 Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. 2x + 3y dx + e…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xy2 dx…

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Q: Calculate the line integral fe F. dr, where F = (ry, x² + y² + z², yz), and C is the boundary of the…

A: Given F→=xy,x2+y2+z2,yz and C is the boundary of the parallelogram with vertices…

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: Consider the curve C between the points (1,0, 1) and (0, 1, 1) at the intersection of the cylinder…

A: To evaluate the line integral along with the curve c of ω=−ydx+xdy+dz.

Q: Use Stokes' theorem to evaluate line integral| (z dx + x dy + y dz), where C is a triangle with…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve.  xy2…

A: Our Aim is to evaluate the line integral along the given positively oriented curve xy2 dx+3x2y dy…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. yex dx…

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Q: Verify the formula fF-T ds = [ (curl F) -n ds in Stokes' Theorem by evaluating the line integral and…

A: According to the given information, it is required to verify the stokes theorem.

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 SF · dr, where F = [e-3y, e², e-2*] and C is the…

A: Given that F=e-3y,ez,e-2x The objective is to find ∫CF.dr. Where C is z=2x2,0≤x≤2,0≤y≤1.

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: 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: 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: 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: Evaluate the integral for y*dx + z²dy + x²dz, where C is the triangular closed path joining the…

A: To evaluate the integral ∫Cy2dx+z2dy+x2dz where C is the triangular closed path joining the points…

Q: (6) Calculate the surface integral SSs F · ñdS where F = (ze", –3ze"V, xy) and S is the…

A: Given that,

Q: Use Stokes' Theorem to find the line integral of F = 3yi + 2zj + 5xk around a 5, oriented…

A: The solution are next step

Q: 344. Use Stokes' theorem to evaluate line integral (zdx + xdy + ydz) , where C is a triangle with…

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Q: Using Green’s theorem, evaluate the line integral ∮Cxydx+ (x+y)dy, where C is the curve bounding the…

A: Given: Where the components of the vector field are

Q: 3. Consider A(r) = (y, -x,0), and the line integral A• dr along the C boundary of the plane x + y +…

A: The given vector function is A(r)=(y,-x,0)., the line integral ∮CA·dr is along the boundary of the…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xy2 dx…

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Q: • Use Green theorem to evaluate the Line integral $(x-3y) da +(42+y) dy whe re C, the Yectungle with…

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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 find the line integral of F = 3yi + 2zj + 5xk around the 25 - (x2 + y) for z…

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Q: Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. P…

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Q: |[-y dx + xy dy]

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Q: Use Stokes' Theorem to evaluate L* + cos x) dx + (sin y + z²) dy + x dz where C is the closed curve…

A: To Evaluate: Use Stoke's Theorem:

Q: Evaluate the line integral in Stokes' Theorem to find the surface integral [[ (V × F) · ndS, where…

A: Given: The vector is Fx,y,z=4y,-xz,exyz. To find: The value of∬S∇×F·ndS by using the line integral…

Q: Use Stokes’ Theorem to evaluate the line integral  ∮  F·d r where F = 〈x^2−z^2, y, 2xz〉, and C is…

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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: 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: Evaluate the line integral ſc F·dr, where F = (y, 0, zy) and C is the helix given by (cost, sint,…

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Q: Use Stokes' theorem to evaluate line integral (z dx + x dy + y dz), where C is a triangle with…

A: Consider the provided question, We have to evaluate the given integral by using the stokes theorem,…

Q: Evaluate the line integral using the Fundamental Theorem of Line Integrals. (3y dx + 3x dy), where C…

A: Given line integral is: I=∫c3ydx+3xdy It can be rewritten as: I=3∫cydx+xdy                ....(1) As…

Q: Verify Stokes's Theorem by evaluating line integral S.F. F(x, y, z) = (-y + z)i + (x − z)j + (x -…

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Q: Use Stokes' Theorem to choose the correct integral to evaluate the line integral…

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

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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: Define stokes theorem and evaluate the line integral SF.r'(s) ds where F = [4z, 2x, 2x], C: the…

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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 F = ( ) and y = {x² + (y – 2)²) = 1 with anti-clockwise orientation. Find line integral , F. ds.…

A: Put x = cost  dx = -sint dt y=sint+2   dy = cost dt int(f.ds)  = int (  y/(x^2 +y^2) dx -…

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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