Let F [e', e', e*] and C be the boundary of the surface S. z=x, 0sx<1,0

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: Use Stokes' theorem to evaluate ∮C z2 ex^2 dx +xy2 dy + tan−1 (y) dz where C is the circle x2 + y2 =…

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

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Q: The equation of the tangent plane to the surface f (x, y, z) = xe cosz - z -1= 0 at the point…

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Q: I F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = (x + y2)i + (y +…

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Q: Let S be the parametric surface, parameterized by r(u, v) = e" cos vi + e" sin vj + uk, (u,v) E D =…

A: given S be the parametric surface, parametrized by  ru,v=eu cosv i^+eu sinv j^+u k^  here…

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: Use Stokes' theorem to evaluate      Scurl(F) · dS. F(x, y, z) = exy cos(z) i + x2z j + xy k,    S…

A: This question is related to vectors, We will solve it using stokes' theorem.

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: CurlF dS x+y' +z =9, z20 se Stokes' Theorem to compute s for the hemisphere intersected with the xy-…

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Q: 63. Verify Stokes' theorem for A = (y - z +2)i + (yz +4)j – xz k, where S is the surface of the cube…

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Q: Calculate the surface integral ∫ ∫ s F ∙ N dS where F (x, y, z) = -y2i + xj + k and S is the shaded…

A: We will find out the required surface Integral.

Q: Use Stokes's Theorem to evaluate [F.dr where F = (z−y)i + (x−z)j + (x−y)k_and the surface S is…

A: Solution :

Q: Use Stokes' theorem to evaluate      CF · dr  where C is oriented counterclockwise as viewed from…

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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. Use Stokes' Theorem to evaluate , Vx F ·n dS where F(x, y, z) = and C is the part of the sphere…

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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: Consider the surface integral хуdS, where S is the surface z = x² + v8 y for 0 < x < 2 and 0 < y <…

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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(x.y.z)=-y²i+xj+z² k, S is the shaded part in the figure at right and C the boundary curve of S…

A: Stroke's theorem: Let S be an oriented smooth surface that is bounded by a simple, closed, smooth…

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: Given F(x, y, z) = -yzi + xzj - xyzk be a vector function that passes through a surface S of z +x? +…

A: Given, Fx,y,z=-yzi+xzj-xyzk be a vector function that passes through a surface S of z+x2+y2=20 that…

Q: Evaluate the surface integral. ds 2 + y32), o s x s S is the surface z = x3/2 0sx < 1, 0 s ys2

A: Given,                        z = 23(x32+y32)and domain D : 0 ≤ x ≤ 1, 0 ≤ y ≤ 2.∂z∂x= 23(32 x) =…

Q: Given: a) F = b) the curve C that is a boundary of the surface z = x² + y? c) the boundary is…

A: Given: F→=&lt;yz, y2, xy&gt;and the curve is the boundary of the surface z=x2+y2 0≤x≤2, 0≤y≤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: - Prove Stokes' Theorem by verifying it for F= [y,z,x] and S the paraboloid. %3D te CEY2=(x, y) = 1…

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Q: Let F(x, y, z) = zi + xj – yk and the curve Cbe the boundary of that portion of the surface S above…

A: Given : vector field F→x, y, z=z i^+x j^-y k^ and the curve C be the boundary of that portion of the…

Q: Use Stokes' theorem to evaluate S curl(F) · dS. F(x, y, z) = exy cos(z) i + x2z j + xy k, S…

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Q: 3. Suppose F z = 4 – a? – y? above the r- y plane, oriented upward. Calculate fe F dĩ in two ways:…

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Q: 3. Consider the surface integral / (Vx F)-n dS, where F = (0, 0, zyz) and S is that portion %3D of…

A: we will draw the surface z=1-x2-y2 and then follow the procedure

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

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Q: Here is a problem where it is challenging to even figure out what the surface looks like. Consider…

A: The solution is in step 2 with clear information and step by step wise.

Q: 2. When F = (y z, xz, x² y?) and S is the part of the paraboloid z = x? + y? that lies in the…

A: First, we have to parametrize the surface to apply the Stokes theorem.  Part of the paraboloid is…

Q: Let F= [e, e?, e*]and C be the boundary of the surface S: z x2, 0sxs2,0sys1. If we use the theorem…

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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: 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: Let F [e, e2, e*]and C be the boundary of the surface S: z=x², 0<xs2, 0sys1. If we use the theorem…

A: Consider the provided question, Let F=ey, ez, ex And C be the boundary of the surface S: z = x2, 0…

Q: 3.2 Calculate the areas of the following surfaces using the differential surface area dS: (a) p =…

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Q: Consider the surface S shown on the graph, whose parameterization is given by: r(u, v) = (v², uv,…

A: Given- Consider the surface S shown on the graph, whose parameterization is given by:  ru, v = v2,…

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: 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 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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Q: Let F-[z, x, 2y'] and C be the positively oriented boundary of the triangle with vertices (0, 0, 0),…

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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…

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