Let S denote the part of the cone z = Vx2 + y? that lies between the surfaces z = 2 + sin(xy) and z = 3 + sin(y), oriented so that the "top" of S points toward the positive Z-axis. Compute SlF - dS, where F(x, y, z) = ( 2v-). 2x+y 2y-a 2z

Q: 1. Calculate the line integral f F-d7, where F (z. y, 2) = -y? +z3 +zk and C is the path C along the…

A: This is a problem from line integral.

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Q: Use cylindrical coordinates to evaluate the triple integral ∫∫∫E √(x2+y2)dV, where E is the solid…

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Q: Calculate F. dS where F = (e" sin y, e² cos y, yz²) S is the surface of the box bounded by the…

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Q: 3 Use polar coordinates to evaluate the integral (3) f[/x² +y° dA Ris bounded by the semicircle y =…

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Q: Q3// A surface S is defined by 2x2 + z 1 and the bounded by the planes y = 0,y 2, x = 0,z = 0 in the…

A: A surface S is defined by 2x2+z=1 which is bounded by the planes y=0, y=2, x=0, z=0 in the first…

Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

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Q: Evaluate the triple integral. 10x dV, where E is bounded by the paraboloid x = 5y? + 5z2 and the…

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Q: Suppose f(x, y, z) = x² + y² + z? and W is the solid cylinder with height 9 and base radius 5 that…

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Q: Calculate F. dS where F = (e* sin y, e² cos y, yz²) S is the surface of the box bounded by the…

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Q: Calculate F. dS where F = (e" sin y, e* cos y, yz“) S is the surface of the box bounded by the…

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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: Calculate F- dS where F = (e" sin y, e* cos y, yz²) S is the surface of the box bounded by the…

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Q: Evaluate the triple integral ∭E(x+2y)dV where E is bounded by the parabolic cylinder y=2x2 and the…

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Q: FD is the region in the first octant between the spheres x2+y2+z²=1 and x2+y2+z²=16, then dV =

A: Converting into spherical coordinates

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Q: The surface area of the solid of revolution generated by rotating 3 x = (y² + 2)ž,1 sys2 about the…

A: Given function is x=13y2+332 where 1≤y≤2. The surface area of revolution of the function is given by…

Q: Evaluate || F-n dS where S is the cylinder (including the disk on the bottom) x² + y² =1 for 0<z<1…

A: First, we plot the given surfaces.Cylinder : x2+y2=1; 0≤z≤1Paraboloid : 3x2+3y2+z = 4; 1≤z≤4.

Q: Calculate F - dS where F = (e" sin y, e" cos y, yz²) S is the surface of the box bounded by the…

A: Given F¯={exsiny,excosy,yz2)

Q: Evaluate the triple integral. SSS 5x²e" dv I where E is bounded by the parabolic cylinder z = 1 - y²…

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Q: Calculate F. dS where F = (e" sin y, e" cos y, yz²) S is the surface of the box bounded by the…

A: We have to find double integral of F. ds

Q: a) Evaluate ||| x²yz dV, where G is solid in the first octant that is bounded by parabolic cylinder…

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Q: 1. Compute the average height of the cone z = a> 0. r² + y² above the disk x² + y² ≤ a² for

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Q: 2) Find the area of the surface r(u,v)=u cos vi+u sin vj+2vk where 0su<3 and 0<vs 2n .

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Q: Compute the scalar line integral xy ds where C is the part of the circle of radius 3, centered at…

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Q: A solid G is bounded by the paraboloid z = 4 – r - y², the cylinder 2+ y = 4 and the plane z = 5.…

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Q: E) Sketch the solid bounded by the cylinder ** +y = 4 and the planes y+z = 4 and z = 0

A: Here, we need to sketch the solid bounded by the cylinder x2+y2=4 and the planes y+z=4 and z=0.

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Q: Compute ,F · dS for F = (xy, 5y,0), S being the cone z² = x + y²,x² + y? 0, with the normal %3D…

A: The vector field is F=⟨xy, 5y, 0⟩ and the parametric equation of the cone is  Rr, θ=rcosθ, rsinθ, r…

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Q: Evaluate the line integral 9x²yzds with respect to s along the 2 curve C: x=t, y = t², z = t³(0 ≤ t…

A: Given: ∫C9x2yzds x=t y=t2 z=23t3 0≤t≤1 To find: Value of the given integral.

Q: Find the plane tangent to the given surfaces at the specific point. f(x, y) = ex(x cos y − y sen y)…

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Q: Compute the line integral (yze"y= + y² + z – 2x) dx + (xze"v² + 2xy) dy + (xye"y= +x+ 3z²) dz C…

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Q: 2)Use Stokes' Theorem to evaluate | F.dr where F =2xyi- yj+2xzk and S is the first octant surface of…

A: The given problem is to evaluate the line integral in the surface of first octant with upward…

Q: Compute the line integral [(yze²v² + y² + 2 − 2x) dx + (xze²v² + 2xy) dy + (xye²³² +x+32²) dz, where…

A: We have to compute the line integral ∫Cyzexyz+y2+z−2xdx+xzexyz+2xydy+xyexyz+x+3z2dz, where C is the…

Q: 2) Use a change of variables to evaluate , zdV; where Dis bounded by the paraboloid z = 16 – x - 4y?…

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