For vector A = < x²yz, xy²z, xyz² >, calculate the surface integral (f, A · ds)

Q: Evaluate the surface integral. y dS, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

A: We have to evaluate the surface integral ∬SydS Given vector equation is r→u,v=ucosv,usinv,v…

Q: Calculate the line integral of f (x, y) =x² +y over the upper half of the unit circle, oriented…

A: A cartesian coordinate system contains two mutually perpendicular number lines named x-axis and…

Q: The vector surface integral j L F • dS is equal to the scalar surface integral of the function…

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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: Evaluate the line integral F dr, where C is given by the vector function r(t). F(x, у, z) y)i (y z)j…

A: Given as

Q: Evaluate the line integral, where C is the given space curve xeZ ds, Cis the line segment from (0,…

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Q: Calculate the vector area of the helicoid parameterised as follows: F(t, s) = (t cos s, t sin s, s)…

A: Please see the below pictures for detailed solution.

Q: Use a calculator or CAS to evaluate the line integral correct to four decimal places. x sin(y + z)…

A: find the explanation below

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

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Q: Let F = (y², x, z²)and S be the part of the paraboloid z = x² + y² with z < 1 and outward facing…

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Q: Evaluate the line integral / V(ry + xz + yz) · dĩ over the curve F(t) = (t, 2t, 3t) for 0 <t < 4…

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Q: Evaluate the surface integral (x + y + z) dS where S is the part of a plane parametrized by S: r(u,…

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Q: Use Stokes' Theorem to evaluate [F•dF.C is the boundary of the portion of :=5-x² - y above the…

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Q: Evaluate the line integral, where C is the given curve. 1 ,C:x =t*, y = t", sis1

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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 the surface integral. y dS, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

A: Consider the provided question,

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: Evaluate the line integral, where C is the given curve. xyeYZ dy, C:x 2t, y = 3t2, z = 3t, osts1 %3D

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Q: pla answer this ASAP,thx Calculate the vector integral(on hte image below) where,F = x 2i + y 2 j ,…

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Q: Evaluate Curlv•ñ , where v = 2xyi + (x² – 2 y)] + xzk and ñ is a unit vector normal to the surface…

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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: Q3 Evaluate Curlv•n , where i = 2xyi + (x – 2y)j+xzk and i is a unit vector normal to the surface…

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Q: Calculate the surface integral // y ds, where S is the part of the helicoid defined by the S vector…

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Q: Evaluate the line integral ∫cF⋅dr, where F(x,y,z)=5xi+yj+3zk and C is given by the vector function…

A: we have given F(x,y,z)=5xi+yj+3zk r(t)=(sint,cost,t)=sint i+ cost j +t k⇒dr=(cost i -sint j…

Q: Let F = . Use Stokes' Theorem to evaluate / curlF · d5, where S is the hemisphere x² + y² + z² =…

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Q: Let S be the surface parametrized by R (u, v) =< u, uv, uv

A: It is given that, the parametrized surface is R(u,v)=u, uv, uv2, 0≤u≤2, 0≤v≤3.  We have to calculate…

Q: Evaluate the surface integral f(r, y, z)dS,

A: answer is in next step

Q: Evaluate the surface integral. y ds, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

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Q: Find the surface area of the surface given by the parametrization F(s, t) = (s – 2t, –2s + 3t, s –…

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Q: Calculate the areas of the following surfaces using the differential surface area dS. 0≤r≤ 4, 60° ≤0…

A: We need to determine the area of the surface: 0≤r≤4, 600≤θ≤900, ϕ=constant using dS.

Q: Find the surface area of the helicoid (spiral ramp) with vector equation r(u, v) = (u coS v, u sin…

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Q: Evaluate the surface integral. y ds, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

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Q: Evaluate the surface integral [[ (a² + y²) dS where S is the surface with vector function r(u, v) =…

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Q: Evaluate the surface integral. y ds, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

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Q: Evaluate the line integral F. dr, where F(x, y, z) = 4xi + 4yj – 5zk and C is given by the vector…

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Q: Evaluate an area of a surface where the vector that is normal to the surface is defined as; d. Q =…

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Q: Calculate the flux integral f(2i + 2j + 2k) · dA where S is a disk of radius 5 in the plane æ + y +…

A: Given F=2i+2j+2k,radius=5 and x+y+z=1 plane

Q: Find the line integral of F = around the curve of intersection of the half cone z = Vr?+y? and the…

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Q: What is the differential for the total surface area of a frustum of a cone with i as the slant…

A: The formula for total surface area of the frustum of the cone with the given slant height l is Total…

Q: Compute the surface integral of the normal component of F(x,y, z) = xi over the triangle with…

A: According to the given information, it is required to calculate the surface integral.

Q: Evaluate the line integral F. dr, where F(x, Y, z) = –xi yj – 5zk and C is given by the vector…

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Q: Evaluate the surface integral f, F. dS where F = 3xyi + 9x²j+3yzk and S is the surface z = xe", 0≤x≤…

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Q: Evaluate the surface integral. (x + y + z) dS, S is the parallelogram with parametric equations x =…

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Q: Let F(r, y) = 4xî + 3yî and let i be the outward unit normal vector to the positively oriented…

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Q: Find the surface area of the helicoid (spiral ramp) with vector equation F(u, v) = (u cos v, u sin…

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Q: Evaluate the integral f/ zye * * dA where R is the first quadrant of the plane. R

A: We know that in the first quadrant of the plane x varies from 0 to infinity and y also varies from 0…

Q: Q3 Evaluate Curlvoñ, where v = 2.xyi +(x² – 2 y)j + xzk and i is a unit vector normal to the surface…

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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: 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.