Use Stokes' theorem to write a line integral that is equal to the surface integral c curl F. ds, where S F(x, y, z) = (-5z, 4x − 3z, 3x +2y), S is the portion of the paraboloid z = 9 - x² - y² above the xy-plane, and its boundary C' is directed counterclockwise when viewed from the first octant. (Hint: parameterize C by the angle 0, when 0 > 0.) Provide your answer below: de

Q: Use Stokes' theorem to evaluate the surface integral I of the two-form w = dŋ, with n = (xz+ yz²) dæ…

A: η=(xz+yz2)dx+(sin(y)+z+5x)dy+xyz dzz=13-x2-y2,   z≥9 F→=xz+yz2i+(sin(y)+z+5x)j+xyzk z=9⇒9=13-x2-y2…

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: Use Stokes' Theorem (in reverse) to evaluate (curl F) •nds where 1.2 F = : 5yzi + 6xj +5yzex²k,S is…

A: Given,        S is the portion of the paraboloid and the unit normal on S points away from the…

Q: Use Stokes' theorem to evaluate 0 F. dr. F(x, y, z) = zexi + (z − 7y³)j + (x − 5z³)k, C is the…

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Q: 3. Let Cibe the circle radius 2 centered at the origin, oriented counterclockwise, let C₂ be the…

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Q: (2) Use Stoke's theorem to evaluate the integral curl where S is the surface given by 2= et-- - 1, 2…

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Q: Verify the formula $ F. T ds = || (curl F) · n dS in Stoke's Theorem by evaluating the line integral…

A: given curve Fx,y,z=9x-5y i +9y-5z j +9z-5x k verify the formula ∮C F·T ds=∫∫σcurl F· n dS in stoke's…

Q: e Il Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = x²z² + y²z²j + xyzk, S is the part of…

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Q: 4. Use Stokes' Theorem to evaluate curl F.dS where F = (x-y, yz, xz) and S is that part of the…

A: Step 1We have, ∫∫curlF.dsStep :2 CurlF=∣∣∣∣∣∣∣​i∂x∂​f1​​j∂y∂​f2​​k∂z∂​f3​​∣∣∣∣∣∣∣​Step 3Here…

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: Verify the formula o F T ds = || (curl F) n dS in Stoke's Theorem. by evaluating the line integral…

A: Given  Fx,y,z=5x-yi+5y-zj+5z-xk We have to verify the Stoke's theorem. x+y+z=3 is the plane.

Q: Verify the Stokes' Theorem in evaluating F.dr if F(x, y, z) = z² i + 2xj- y³ k, where C is the…

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Q: Compute the surface integral of the function f(x, y, z) = 2xy over the portion of the plane 2x + 3y…

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Q: Question 6 Prior to running the Boston Marathon, a runner's personal best pace for a race is 10…

A: Given that Prior to running the Boston Marathon, a runner’s personal best pace for a race is 10…

Q: Use Stokes's Theorem to evaluate e curlF. ds. (1) F(x, y, z) = x²y³zi+sin(ryz)j + xyz k, S is the…

A: “Since you have posted multiple questions, we will provide the solution   only to the first question…

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: F(x, y, z) = tan-'(x?yz²)i + x²yj + x²z?k, S is the cone x = V y2 0 <x < 4, oriented in the…

A: Define curve C with boundary curve: r→=4i^+4costj^+4sintt^

Q: 9. If F = (x – z) î + (x³ + yz)ĵ + 3xy² k and S is the surface of the cone z = a – Va? +y?) above…

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Q: Use Stokes' theorem to write a line integral that is equal to the surface integral cu aff curt S…

A: We know that Stokes theorem, let S be oriented smooth surface that is bounded by simple closed…

Q: Evaluate the line integral PF • dr by evaluating the surface с integral in Stokes' Theorem with an…

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Q: Use Stokes' Theorem to evaluate |/ curl F. dS. F(x, y, z) = tan-(x²yz²)i + x²yj + x²z?k, S is the…

A: Stokes' Theorem:                                 ∮C F .dr =∬S curl F. dS Where C is the boundary of…

Q: Use Stoke's theorem to evaluate the integral [[ curl where S is the surface given by and 2 = 64-x²-y…

A: The stoke's theorem states that ∫∫S∇×F·dS=∫CF·dr, where C is the boundary of the surface S. Consider…

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: (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = U-v, z = 1+2u+v, 0 ≤…

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Q: Evaluate f (x-y) dV, where E is the solid E in the first octant bounded by the surface z=1-² and the…

A: In the given problem we have to evaluate the integral                                       where…

Q: Use Stokes' theorem to evaluate f curlF · ds. F(x, y, z) = y²zi+xzj + x²y²k S is the part of the…

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Q: (b) Use Stoke's Theorem to evaluate the line integral $ (3? – 22) dr + (z² – x²) dy + (y² – x²) dz,…

A: Stokes theorem  ∮CF.dr=∫∫SCurl F .dS Where S be a smooth surface that is bounded by a  closed,…

Q: Use Stokes' theorem to evaluate the surface integral ff(V x F). dS F = yi-xj+exp(xz)k and S is the…

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