Calculate || F. dS where S F = (3xy?, xe², z*) S is the surface of the solid bounded by the cylinder y? + z2 = 4 and the planes 5 and x = 4

Q: Evaluate the surface integral F. ds where F = 5xyi +8x²j+ 5yzk and S is the surface z = ïe², 0 ≤ x ≤…

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Q: 3) Evaluate the surface integral. I| (x²z+ y²z) ds where S is the part of the plane z = 4 + x +y…

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Q: Evaluate the surface integral fs F. dS where F = (4x, -2z, 2y) and S is the part of the sphere x² +…

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Q: Find the area of the surface S where S is the cap cut from the paraboloid z = 2– x – y by the cone z…

A: Given that : z=2-x2-y2z=x2+y2 Now, to find the point of intersection , 2-x2-y2=x2+y2Put…

Q: Evaluate JS yz + 4ryds where S is the surface of the solid bounded by 4x+2y+z=84, z=0, y=0 and x=0.…

A: Use the divergence theorem to find the surface integral,…

Q: Evaluate fR z = Jx2 + y2 x2 + y2 + z2dxdydz, where r is the region bounded by the plane z = 3 and…

A: We will convert integral into spherical co ordinate system . 1st relation between cartesian and…

Q: b) Given F(x, Y, z) = (x³ + cosh z) i+ (2y³ – 3x²y)j – (x² + 4y²z) k. Use Gauss's theorem to…

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

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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: Calculate F . dS where F = (4x°z, 4y°z, 3z*) S is the surface of the solid bounded by the…

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Q: Evaluate the surface integral.∫∫S (x2+y2+z2) dS, S is the part of the cylinder x2+y2 = 9 between the…

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Q: Evaluate the surface integral| f(x.y.z) dS using an explicit representation of the surface. f(x.y.z)…

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Q: Evaluate the surface integral. z2 S is the part of the paraboloid x = y2 + z² given by 0 sx 5 4 1 V5…

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Q: b) Given F(r, y, z) = (x³ + cosh z) i+ (2y - 3ry)j – (x² + 4y²z) k. Use %3D Gauss's theorem to…

A: 1. The divergence is an operator, which takes in the vector-valued function defining this vector…

Q: Calculate F . dS where F = (4x°z, 4y°z, 3z*) S is the surface of the solid bounded by the…

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Q: Calculate ff F.n dS where F x'yzi + 2xj + y?k in the solid region S bounded by the parabolic tube z…

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Q: Q11// If F = 3xi + 2j – k , Evaluate , F dv where V is region %3D bounded by the plane y=D0,z30,…

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Q: * Evaluate the surface integral SS F - d§, where F = z7 + y²7 + z² and S is the boundary of the…

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Q: Calculate F.dS where F = (3ry", re", z*) S is the surface of the solid bounded by the cylinder y + z…

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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: Which of the following represents the area of the surface cut from the plane z = ax + by by the…

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

Q: (a) Evaluate the following surface integral yex²+z² dS, where o is the portion of the surface of the…

A: Given the integral ∬σyex2+z2dS we have evaluate the given surface integral where σ is the portion of…

Q: Let o be the portion of the paraboloid F(u, v) = u cos(v)i+u sin(v)j+ u*k for which 0 < u< sin(v), 0…

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Q: Evaluate the surface integral: || G(x, y, z) ds for G(x,y,z) = z², where S is the portion of the…

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Q: #3. Evaluate the surface integral xz ds, where S is the part of the plane 2x +2y +z = 4 that lies in…

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Q: Use Stoke's theorem to compute the integral SL(V × F) · n dS, where F(x, y, z) = (xz, yz, xy) and S…

A: We have to compute ∬(∇×F)·n dS , where F(x,y,z)=(xz,yz,xy) and S is the portion of the sphere…

Q: 3. Let S be the surface of the solid region above the ry-plane and bounded between the planes r + z…

A: Here,  F⇀=z,ex,1+yz

Q: b) Given F(x, y, z) = (x³ + cosh z) i+(2y³ – 3x²y) j – (x² + 4y²z) k. Use Gauss's theorem to…

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Q: 3Af F=x1-yj+(z- 1) k, V is the volume of the cylinder bounded by z = 0, z = 1 and x +y = a° and S is…

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Q: Evaluate F. dS where: F(x, Y, z) = yi+xj+ zk, S is the boundary of the solid region E enclosed by…

A: Given F⇀x,y,z=yi^+xj^+zk^ To find ∫∫SF.dS: The divergence theorem states that ∫∫SF.dS=∫∫∫V∇.F dV…

Q: Let F(r, y, z) = r²i+ y²j+ z²k and S the surface of the region bounded by 5. the cylinder 1? + y² =…

A: Divergence theorem

Q: Use Stokes's Theorem to evaluate f. F dř where F(x, y, z) = (x- y) i+ (y-z)j+ (z - x) k and S is the…

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Q: Use Gauss’ theorem to evaluate F.ndS for the given F and o. (b) F(x, y, z) = x³ i+x?yj+xy k, o : the…

A: We will use gauss divergence theorem to find value of given surface integral  If E is a  simple…

Q: (a) Let S be the surface z2 = x² + y? bounded between the planes z = 0 and z = 2. Evaluate (z –…

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Q: (b) Evaluate the surface integral ƒ (x, y, z)dS where f(x,y, z) = z² and S is a portion of the cone…

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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: Evaluate the surface integral. ∫∫s(x2 + y2 + z2) dS, S is the part of the cylinder x2 + y2 = 9…

A: To evaluate :  ∫∫s(x2 + y2 + z2) dS, S is the part of the cylinder x2 + y2 = 9 between the planes z…

Q: please help me as soon as possbile

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

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Q: Let E denote the part of the plane x + y + z = 1 that is inside the cylinder r? + y? = 1. Compute…

A: We have to find the value of  ∬ F→.dS→

Q: 3.Evaluate || F. ds where F= zi+x j +y k and 'S' is the surface of the cylinder x'+ y=1 contained in…

A: Given that ∬S F→·dS→ where  F→=z i^+x j^+y  k^ .......1and  S is the surface of the cylinder x2+y2=1…

Q: Calculate F. dS where F = (3xy°, xe", zª) S is the surface of the solid bounded by the cylinder y? +…

A: Let's find.

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: Let A = 6 zi + (2x + y)j – x k ; Evaluate A.ndS over the entire surface S of the region bounded by…

A: Please see the figure below to comprehend what's going on:

Q: 1. Evaluate the surface integral [[' xz² ds ; o is the part of the cone z = x² + y² that lies…

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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: Evaluate [F d$ for F = yi+=j+2xk and S is a surface of the region bounded by the cylinder x+ y = 4…

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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: Q2// A surface S is defined by x? + z = 9 and the bounded by the planes y = 0, y = 1,x = 0, z = 0 in…

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