Verify the Divergence Theorem by evaluating F.N ds as a surface integral and as a triple integral. F(x, y, z) = (2x – y)i – (2y – z)j + zk S: surface bounded by the plane 2x + 4y + 2z = 12 and the coordinate planes 8 6. 00 4 y 8 2)

Q: /F-nds, where b) Use Gauss theorem to evaluate F(x, y, z) = (2a²y² + In 2) i – xy° j – tanh(2² + y²)…

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Q: Evaluate f. F.dr, where F(r, y, z) = z?i+rj and C is the boundary of the square {(r, y, z)|0 < x <…

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Q: b) Given F(r, y, z) = (r³ + cosh z) i+ (2y3 – 3r*y)j – (2² + 4y²z) k. Use Gauss's theorem to…

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Q: Use Stoke's theorem to evaluate the integral xydx +2x 'dy-&r 'zdz where C is the boundary of the…

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Q: 8. Choose, refer and use one of the theorems of Vector Calculus to evaluate the line integral F- ds…

A: To find- Choose, refer and use one of the theorems of the Vector Calculus to evaluate the Line…

Q: L₂F F = (4x³z, 4y³z, 3z¹) S is the surface of the solid bounded by the hemispheres 16 — x² - y², z =…

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Q: Compute the surface integral s F-ndo. F = xyi - x¹j+ (x+z)k. The surface is the top of the plane 2x…

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Q: Verify the formula $ F. T ds = || (curl F) · n dS in Stoke's Theorem by evaluating the line integral…

A: given curve Fx,y,z=9x-5y i +9y-5z j +9z-5x k verify the formula ∮C F·T ds=∫∫σcurl F· n dS in stoke's…

Q: A new flag pole for a school campus measured 25 2/3 feet. It was put 4 1/2 feet into the ground and…

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Q: . Evaluate the integral: ſf (V · n) da over any surface whose bounding curve is in the (x, y) plane,…

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Q: Let Y be the portion of the sphere x² + y² + (z − 2)² = 4 which lies below the plane z = 3 with…

A: Given  ∫Cz2+3yi→+2z-2xj→+z2k→.dr→ The portion of the sphere x2+y2+z-22=4 and plane z=3

Q: Verify the formula o F T ds = || (curl F) n dS in Stoke's Theorem. by evaluating the line integral…

A: Given  Fx,y,z=5x-yi+5y-zj+5z-xk We have to verify the Stoke's theorem. x+y+z=3 is the plane.

Q: Evaluate the surface integral G (x, y, z) dS C where G (x, y, z) = x – y – z, and C is the…

A: Given: Gx,y,z=x-y-zRu,v=u-v,v-uu-3v-10≤u≤20≤v≤3 Find: ∫∫CGx,y,zdS Formula used: ∫xndx=xn+1n+1∫dx=x

Q: Use Stokes' Theorem to evaluate F. dr, where F(x, y, z) = xzi+ xyj+2xz k,•. and C is the boundary of…

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Q: b) Use Gauss theorem to evaluate F.ndS, where F(r, y, z) = (2x²y² + lIn 2) i – ry° j – tanh(x² + y³)…

A: Given function  F(x, y, z) = (2x2y2+lnz)i -xy3j -tanh(x2+y2)k we have to find ∬σF.nds by using guass…

Q: be the surfa enned by the vector function R(u, v) (-/- 2u,v + 5, ve¹) all (u, v) € R². Set - up an…

A: Here, in the question given a surface S defined by the vector function: R ⇀(u, v) =(v5-2u, v+5, veu)…

Q: · ƒ [‚²³ · F . S F = (4x³z, 4y³z, 3z¹) Calculate dS where and S is the surface of the solid bounded…

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Q: 2- Use Gauss's divergence theorem to evaluate the surface integral || (ry dydz + 2y°dædz + y°…

A: To evaluate the surface integral: ∬Sxy2dydz+2y3dxdz+y2zdxdy

Q: Evaluate the integral FdS, dS upwards S With F(x, y, z) = (x−y, 2z, y-x),where S is the surface…

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Q: Consider the surface integral хуdS, where S is the surface z = x² + v8 y for 0 < x < 2 and 0 < y <…

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Q: 6. Use the divergence theorem to determine the surface integral of the vector function F on the…

A: The given problem is to evaluate the surface integral of the given vector field over the given…

Q: 8. Let F = xyzi + (y² + 1)ĵ + z³k and S be the surface of the cube 0 < x, y, z < 1. (a) Evaluate the…

A: Given that F→=xyzi→+y2+1j→+z3k→ S be the surface of the cube 0≤x,y,z≤1 Now,…

Q: a) Find the curl V×Fif F = (y',2xy,yz)

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: Evaluate G if G is a solid in the first octant bounded by the plane y +z = 2 and the surface y = 1–…

A: Use the following formulae, to obtain the solution. a-b2=a2-2ab+b2∫xndx=xn+1n+1+C

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,…