Completely set up (but do not solve!) the surface integral over the given oriented surface: F = (y°, 3, –x) with the portion of the plane r + y + z = 1 in the octant (r, y, z > 0), with the upward-pointing normal.

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: Evaluate the surface integral. xyz dS, S is the cone with parametric equations x = u cos(v), y = u…

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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: Evaluate the surface integral f F. dS where F = (-2x, –5z, 5y) and S is the part of the sphere x2 +…

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Q: Evaluate the surface integral. xyz ds, S is the cone with parametric equations x = u cos(v), y = u…

A: See the attachment

Q: Set up, but do not evaluate, an iterated integral that equals the surface integral |/ (2² – y²) dS,…

A: Given data:   The given surface integral is I=∫∫S(z2-y2)dS. The given part of the cone is…

Q: Evaluate the surface integral. xyz dS, S is the cone with parametric equations x = u cos(v), y = u…

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Q: Consider the surface S which is the part of the cylinder x^2 + z^2 = 9 , whit   0 ≤ y ≤ 2; x ≥ 0; z…

A: a  x2+y2=9    0≤y≤2,  x⩾0, z⩾0   S is parametrised by     rθ,y=3 cos ϖ, y, 3 sin θ    θ∈0 π2,   y∈0…

Q: Evaluate the surface integral (V x F). n ds where S is the portion of the tetrahedron bounded by r…

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Q: Evaluate the surface integral + y² + 6z² ) d$ where S is the part of the cone z = 6 - Vx? + y above…

A: Calculate ∫∫Sx2+y2+6z2dS; wherethe surface S is a part of the cone z=6-x2+y2above the z=0 plane.Then…

Q: Evaluate the surface integral [[ F.ds where F(x, y, z) = (x³ +y³) i+(y³+z³) j+(z³+x³) k S and S is…

A: We will calculate surface integral , use of divergence theorem

Q: Evaluate the surface integral. The double integral over S (xz) dS, S is the part of the plane…

A: Evaluate  the surface integral for the function2x+2y+z=4

Q: Compute the surface integral over the given oriented surface: F= y'i + 6j – zk, portion of the plane…

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Q: Evaluate the surface integral. xyz ds, S is the cone with parametric equations x = u cos(v), y = u…

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Q: Compute the surface integral over the given oriented surface: F = y²i+6jxk, portion of the plane x +…

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Q: (b) Use Stokes' Theorem to find the surface integral over the positively oriented upper hemisphere…

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Q: Evaluate the surface integral. 2,2 ds S is the part of the cone + y that lies between the planes z =…

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Q: The portion of the surface h x² + y? with h, a > 0, 2 = -. a between the ry-plane and the plane z =…

A: Given that:   The portion of the surface is given as: z=hax2+y2  with h,a>0

Q: (b) Verify Stokes' theorem on a region which is a portion of the sphere x? +y? +z² = 16 which lies…

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Q: Let o be the portion of the plane x + y = 1 that is in the first quadrant and is between the…

A: Let be  the portion of the plane x+y  = 1 that is in the first quadrant and is between the…

Q: Evaluate the surface integral. z ds S is the surface x = y + 2z?, 0 s ys 1, 0 s z 5 5

A: We are given that S is the surface x=y+2z2, 0≤y≤1, 0≤z≤5. Since, 0≤y≤1, 0≤z≤5, then 0≤x=y+2z2≤51.…

Q: Evaluate the surface integral || x2 z2 dS, where S is the part of the cone z2 = x² + y?, S that lies…

A: Here we solve the given problem of calculus.

Q: Use Stokes's Theorem to calculate the surface integral S Ss F - dS where F(x, Y, z) = xi + (2ze² –…

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Q: SS curl F · dS =0 S

A: we have to prove that if a surface is closed then the surface integral of curlF .ds is 0 Here…

Q: (² + y*)% ; + =4k and let S be the surface of the solid 1) Let F(r, y) = cone given by z = V²+y²,…

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

A: Consider the given surface integral, ∬Sx+y+zdS Substitute the values x=u+v, y=u-v, and z=1+2u+v in…

Q: Use Stokes's Theorem to calculate the surface integral / Ss F · dS where F(x, y, z) = xi +(2ze* –…

A: Given the vector field Fx,y,z=x,2zex-y,y. And S is a part of the ellipsoid 4x2+4y2+z2=17 between z=1…

Q: The surface integral A. dS where Ā = xi+yj+zk closed surface S is defined by sphere

A: Introduction __:

Q: Evaluate the surface integral of G(x, y, z) = z - y over the surface S, where S is the portion of…

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Q: Find the surface area of the cone z = x² + y2 that lies between the plane y = x and the cylinder y =…

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Q: ordinates to find the volume

A: Given surface: z=e-x2-y2-e-9 and XY plane To find: Using polar coordinates, find the volume of the…

Q: Evaluate the surface integral. xyz dS, S is the cone with parametric equations x = u cos(v), y = u…

A: Evaluate the surface integral.

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

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Q: Use Gauss's Theorem to find the surface integral OF •dS across the positively-oriented S sphere of…

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Q: Find the surface area of the cone z = ' + y² that lies between the plane y = x and the cylinder y =…

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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: Find the surface area of the plane 3x + 2 y + z = 6 that lies in the first octant.

A: The surface area of the plane z=f(x,y) is given by the formula                          S=∬D…

Q: Evaluate the surface integral. xyz dS, S is the cone with parametric equations x = u cos(v), y = u…

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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: Compute the surface integral over the given oriented surface: F = (0,6, x²), hemisphere ? + y² + z²…

A: Given function is F=0,6,x2 To find the surface integral of the above function over the below…

Q: The parametric surface R (r, 0) = A = ) = r cos (i + r sin 0j + 0k, for 0 ≤ 0 ≤ 6π, 0 ≤ r ≤ 1, is a…

A: Given parametric surface  R→r,θ=rcosθi+rsinθj+θkfor 0≤θ≤6π, 0≤r≤1

Q: Consider the surface S which is the part of the cylinder x^2 + z^2 = 9 , whit   0 ≤ y ≤ 2; x ≥ 0; z…

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Q: use the Causs theorem to reduce the surface integral (JA.ds) on all six faces of a cube whose volume…

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Q: Evaluate the surface integral [(xz + y* ) ds where s is the surface of the XZ- cylinder y + z? =…

A: Consider the provided question,

Q: Jevaluate the surface integral ff, (y²z2 i+ z?x² j+ z²y²k).n ds, where S is the part of the sphere…

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Q: Let S be the part of the cylindrical surface x2 + y2 = 4 limited by the plans z = 0 and z = y + 2.…

A: Let S be the part of cylindrical surface x2+y2=4, limited by z=0 and z=y+2 The formula to find the…

Q: need ASAP B. Find the area of the portion of the cylindrical surface y = 4 − x2 in the first…

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Q: Evaluate the surface integral s F. dS where F (-x, -4z, 4y) and S is the part of the sphere x? + y?…

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

A: here, f (x, y,z) = x + y + z the parametric representation of the surface S  x = u + v y = u -v z =…

Q: Evaluate the surface integral. (x²z. y?z) as x2z + S is the hemisphere x2 + y2 + z² = 4, z 2 0

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