2. Evaluate F.ndS for the given F and o. (a F(x, y, z) = xi+ yj+zk, o: the surface of the sphere x² + y² + z² = 4. %3D

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Q: 3. Evaluate , (x + z)dS where the surface S is the first-octant portion of the cylinder y² + z² = 9…

A: Step:- 1 Since, we know Surface integrals ∫∫Sf(x,y,z)dS=∫∫Df(x,θ) rx×rθ dxdθ…

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Q: b) Use Gauss' theorem to evaluate f[ F· ndS where M UTM = (x² – y)i + y°z²j + (xy – y²z³)k and o is…

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Q: 18. Evaluate § (9 − x² − y²) dV, where H is the solid hemi- sphere x² + y² + z² ≤ 9, z ≥ 0.

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Q: Verify Stoke's for F = (2x – y)i – yz²j – y²zk where S is the upper half of the sphere x? + y? +z² =…

A: Solution is given below

Q: Evaluate F.ndS for the given F and o. (b) F(x, y, z) = (x² + y) i+ xyj– (2xz + y) k, o: the surface…

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Q: Evaluate f(x,y,z) dS 2. 3DX²+4y+z on the surface S {(x,y,z):05xS2, y= 3, 1Sz5 4)

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Q: a) Evaluate x²z dS where o is part of a sphere x² +y² + z² = 8 above %3D the plane 2.

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A: Let's find.

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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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A: Thanks for the question :)And your upvote will be really appreciable ;)

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Q: S y = 3 – 2 4z – 4 = 3(x +1)?

A: Let us start solving the problem step by step

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Q: Consider the surface S given by: S :r(u, v) = (uv², u + v, v³), u E [0, 1], v E [0, 2]

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Q: 7. D is bounded by the surface (a2 + y² + z²)² = a²(x² + y? – z²). %3D

A: Sol

Q: 15. The solid enclosed by the sphere x2+ y2 + z2 = 4a? and the planes z = 0 and z = a. %3D

A: Given: x2+y2+z2=4a2          ... (1) z=0z=a

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Q: 17. F = |r|r, where r = xi + yj + z k, S consists of the hemisphere z = /1 – x² – y2 and the disk x?…

A: The solution are next step

Q: 6. If S is the surface of the sphere x + y² + z? = 9. Prove that curl F- ds = 0. %3D

A: Solution:-

Q: (a) Given that F(x,y,z) = (3x² + 3y²)i – 2xyj + yzk, evaluate S, F·dr for which C is the boundary of…

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Q: Evaluate F. dS, where F = 6xy²i + 6x²yj + 2z°k and S is the surface of the unit sphere.

A: