EXERCISES 2.10 1. Use Stokes' Theorem to evaluate F.dr for E = (xz,-y,x²y), where C is the boundary of the open surface, S that bounded by x =0, y = 0 and 2x+ y+2z = 8, which is not include xy- plane.

Q: 23. Use Stokes' theorem to evaluate Se F · dr, where F(x, Y, z) = (xy, yz, zar) and C is the…

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Q: Calculate F · dS where F = (e* sin cos y, yz?) y, et and S is the surface of the box bounded by the…

A: By using the divergence theorem, we can make equality between the surface integral of a function and…

Q: Evaluate e dV where E is enclosed by the paraboloid z = 4+ x² + y?, the cylinder E x2 + y? = 1, and…

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Q: If E is the solid shape bounded by x 2 0,y 20 ,z 2 0 and the plane 2x + 3y +z = 6 evaluate (x + y)…

A: The given question is solved below

Q: Compute the line integral ∫_C F · dr, where F (x, y) = 〈−x^3, xy〉 and C is part of circle x^2 + y^2…

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Q: EXERCISES 2.10 1. Use Stokes' Theorem to evaluate E.dr for F=(xz,-y,x²y), where C is the boundary of…

A: Given: F=<xz,-y,x2y> C surface, S is bounded by x=0, y=0 and 2 not include xy-plane Now,…

Q: Q#5. Evaluate the surface integral ff(x,y,z)dS When f(x, y, z)= 3xyz and is the portion of the plane…

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Q: 5. Evaluate the surface integral S_(x+ y) ds ; o is the part of the plane 2x + y +z = 3 that lies in…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 5+x +y, the cylinder a2 + y = 1, and the xy…

A: The objective is to evaluate ∫∫∫EezdV, where E is enclosed by the paraboloid z=5+x2+y2, the cylinder…

Q: Verify Formula (1) in the Divergence Theorem by evaluating the surface integral and the triple…

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

A: Given Data: Integral: ∬SF→·dS Vector: F→=exsiny, excosy, yz2 Planes: x=2, y=4, z=3 The divergence of…

Q: Find the value of the integral fs (V x A). da if the vector A = yi + zj + xk and Sis the surface…

A: Given the vector A=yi+zj+xk and S is the surface defined by the paraboloid z=1-x2-y2

Q: (a) Compute directly I = S Ss F-dS, where S is the surface of the sphere x? +y? +z? = 4 and F =…

A: X²+y²+z²=4=2² Therefore radius of sphere is 2.

Q: Evaluate /// 203 dV G if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: Here we have to find range of values for x,y and z and then find triple integral

Q: Consider the solid E determined by the inequalities x² + y² + z≤ 4, and let S denote the surface…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate ez dV where E is enclosed by the paraboloid z = 4 + x? + y², the cylinder x? + y? = 1, and…

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Q: Page: 100 EXERCISES 2.10 1. Use Stokes' Theorem to evaluate F.dr_ for F=(xz,-y,x²y), where C is the…

A: Given the vector field F=xz,-y,x2y and the surface S is bounded by x=0,y=0,2x+y+2z=8.

Q: Let M = { (x; y; z)TER3: x2 + y2 < 5,0 <z <2,x<ys0}R3. By which one Expression is a parameterization…

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Q: (4) Use Stokes' Theorem to evaluate 11. Vx (yz, xz, xy) dS where S is the surface S that is the part…

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Q: Evaluate xy dV where E is bounded by the parabolic cylinders y = x², x = y² E and the planes z = 0…

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Q: (4) Consider the following set: S = {(x, y, z) E R | xy + yz + x = -2}. (a) Show that S is a…

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Q: F. dS, where F(x, y, z) = z²xi + 2) + (x2z + y2)k and S is the top half of the sphere x² + y² + z? =…

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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: 16. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…

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Q: A surface x(y, z) is defined implicitly xy + yz +x'z' = 3-xZ Calculate ду

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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: 4. (Section 17.8) Use the Divergence Theorem to calculate [[F F-dS, where F = y + ryj – zk and S is…

A: To use the divergence theorem to calculate ∫∫SF⋅dS.

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: Verify Stoke 's Theorem for F = (x² +y – 4) î + 3 xyj + (2 xz + z²) k over the surface of hemisphere…

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Q: Evaluate the triple integral (* + 1y) dV where E is bounded by the parabolic cylinder y = 32² and…

A: We have to find the triple integral  ∫∫∫E(x+y)dVwhere E is bounded by the parabolic cylinder y=3x2…

Q: Use Stokes' Theorem to evaluate F. dr, where F(x, y, z) = zi + yj – rk and C is the boundary of the…

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Q: 10/ Compute e Fids, where S is the surface z =N16-x²-y² oriented up ward and F = <y,-x, zZ %3D 工=?

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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: A solid G is bounded by the paraboloid z = 4 – x2 – y?, the cylinder x2 + y? = 4 and the plane z =…

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Q: Evaluate x dV , where E is the E region in the first octant bounded by the sphere x² + y² + z² = 1…

A: given region is in the first octant. using spherical coordinates x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ and…

Q: Q4// A surface S is defined by x2 +z = 1 and the bounded by the planes y = 0,y = 2,x 0,z = 0 in the…

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Q: (a) Compute the surface integral || a xy dS, where S is the quarter cylinder x2 + y? = 1; x, y > 0…

A: Given that The surface integral is ∬Sxy dS, where S is the quarter cylinder x2+y2=1; x,y≥0 between…

Q: Let S be the piece of the surface z = 9– x2 that lies inside the cylinder x2 +y? = 9, and let F =…

A: According to question, Given Surface, z = 9 -x2 ,This surface lies Inside the cylinder x2 + y2 = 9,F…

Q: Evaluate (x + 5y) dV where E is bounded by the parabolic cylinder y = x² and the planes z = 3x, y =…

A: given is  a partial differential equation in dX , dY, dZ we can partially integrate the given…

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.

Q: Let S denote the part of the cylinder x2 + y² = 9 that lies between the planes r + y = 1 and x – y =…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 4 + x² + y², the %3D cylinder x? + y² = 3,…

A: We need to evaluate integral.

Q: #6. Use Stokes' Theorem to evaluate S. F dr, where F(x, y,2) = i+(x + yz)j+(xy-V) k and C is the…

A: Given that, Fx,y,z=i+x+yzj+xy-zk and C is the boundary of the part of the plane 3x+2y+z=1 in the…

Q: Verify Stokes' Theorem for F = xyî + yzj + xzk and where s is the surface of the paraboloid z = x² +…

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Q: Use Stokes' Theorem to evaluate ∫CF⋅dr where F(x,y,z)=xi+yj+3(x2+y2)k and C is the boundary of the…

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Q: Evaluate e dV where E is enclosed by the paraboloid z = 5 + x? + y?, the cylinder x? + y? 5, and the…

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Q: Use Stokes’ Theorem to evaluate F(x, y, z) = 3zi + 4x j + 2yk; C is the boundary of the paraboloid…

A: Use Stokes theorem

Q: Sketch the reglons enclosed by the glven curves. y = Vx, y= X= 16 y y 6 4 4 3 3 2 10 15 10 15 O-1…

A: Given : y = √x  y = 1/3 x  x = 16

Q: Evaluate e dV where E is enclosed by the paraboloid z = 5 + x + y°, the cylinder + y = 1, and the ry…

A: To Determine: evaluate ∫∫∫eZdV  where E is enclosed by the paraboloid z=5+x2+y2,the cylinder…