(6) Use the Divergence Theorem to evaluate dS, where F(x, y, 2) = xyi + (y² + e*=*)j + sin(xy)k and S is the surface of the region E bounded by the parabolic cylinder z = 1 – a? and planes z = 0, y = 0 and y + z = 2, as shown below;

Q: Q1: Evaluate: 2x dV where E is the region under the plane 2x + 3y + z = 6 that lies in the first…

A:

Q: Let S be the closed cylinder bounded by the surface r2 + 2² = 4, and the planes y = 1 and y = 4. Use…

A: Let's find.

Q: 3.4.13 Verify the divergence theorem [[ F. JS = [] F.dS div F dV S for F = 4xi-2y²j+z²k over the…

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Q: 4. Find the outward flux of F = (0,0, ze"e-) across the boundary of the region D where D: the cube…

A: We need to find the outward flux of F = <0, 0, zexe-y> across the boundary of the region D…

Q: 17. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…

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Q: 2. Evaluate the integral // xz? dy dz + (x²y – 2³) dz dx + (2xy+ y²z) dx dy where S is the surface…

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Q: Ise the Divergence Theorem to find the outward flux of F = (9x + 9xy²) i+ (6y³ + 3e" sin z) j+ (92°…

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Q: 5. Use the Divergence Theorem to evaluate [[F•d$ where F = yx² i +(xy² - 3=*)j+(x² + y² )k and S is…

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Q: Q1. Verify Divergence theorem for the function F = ēpp over the semi-cylindrical volume x2 + y? < a…

A: Given:- →F=→eρρ V=x2 +y2≤a0≤z≤h,x≥0

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

A:

Q: 5xy dv, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by…

A: The given integral is ∭E5xydV. The region E lies under the plane z=1+x+y and above the region in the…

Q: use the divergence theorem to compute: F(x,y,z)=x2i+y2j+z2k; for the boundary of the solid region…

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Q: Use the Divergence Theorem to evaluate ff F-n do where S F(x, y, z)=(x² +cos yz, y-e², z² + x²) and…

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Q: Verify the divergence theorem for F = 3 i + xy j + x k taken over the region bounded by z = 4 −…

A: According to the given information, it is required to verify the divergence theorem for,

Q: (1) Use the divergence theorem to evaluate F-S. where F (z, y, 2) = zzi – j+4:k and S is the surface…

A: we use divergence theorem for finding the surface integral.

Q: e dV where E is bounded by the parabolic cylinder z = 1 -y and the planes Evaluate the triple…

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Q: Use divergence theorem to evaluate where F(x, y, z) = 3xyi + xyj + 2zk and s is the surface of the…

A: Given ; F(x,y,z) = 3xyi + xyj + 2zk

Q: 3. Use the Divergence Theorem to evaluate F.dS where F = -zyi+(z – 1) j +k and S is the surface of…

A:

Q: 1. Use the Divergence Theorem to evaluate /| F.dš where F.dSv F = yx? i+ (xy? - 324) j+ (x³ + y?) k…

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Q: (15) Use the divergence theorem to evaluate SSF. ds, where S 3 F(x, y, z) = and 5 is the surface of…

A: To evaluate the given integral using divergence theorem.

Q: 387. Use the divergence theorem to calculate surface integral F. dS when F(x, y, z) = x²z³i+ 2xyz³j+…

A: Given that: F(x,y,z)=x2z3i+2xyz3j+xz4k and S is the surface of the box with vertices (±1,±2,±3).

Q: Verify the divergence theorem for F=3i + xy j + x k  taken over the region bounded by z = 4 - y^2 ,…

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Q: II.F F.ds where S is the piecewise smooth surface of the tetrahedron with vertices (0, 0, 0), (1, 0,…

A: If F is a continuous differentiable vector point function in the volume V, bounded by the closed…

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

A:

Q: Verify Gauss Divergence Theorem for F = xy²î + yx²j+ek for the solid region D bounded by z = √x² +…

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Q: Q3. Verify the divergence theorem for F = 3 i+ xy j+x k taken over the region bounded by z = 4 – y?,…

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Q: Verify the Divergence Theorem by evaluating [[F. F. N ds as a surface integral and as a triple…

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Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = (6x2…

A:

Q: 3. Evaluate /// 2* dV if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: triple integral

Q: 5/ MATH

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Q: Verify the divergence theorem for F = 3 i+ xy j + x k taken over the region bounded by z = 4 − y2, x…

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Q: According to the divergence theorem, one of the following integrals represents the surface integral…

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Q: 17. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…

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Q: (3) Verify the divergence theorem where (a) F(x, y, z) planes x = 0, x = 1, y = 0, y = 1, z = (b)…

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Q: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = 2xz i…

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Q: I have trouble getting to the answer. Just wondering if I can get it step by step.

A: Consider the region for solid.Let the solid be bounded by the coordinate planes and the plane 2x +…

Q: b) Use the divergence theorem to compute ff, F · i ds, where S is bounded by x +y + 2z = 2 located…

A:

Q: 4. Evaluate the surface integral ff. F.dS by the divergence theorem where F = (3xy2, yx? -…

A: S is the surface x2+y2≤25, 0≤z≤2 So surface S is a cylinder with radius 5 as shown in below figure.…

Q: Verify the Divergence Theorem: ls F- dS where F= (3z + z",y – sin zz, 2z+ ye) and Sis surface of box…

A: We need to find integral using divergence theorem.

Q: Use the Divergence Theorem to evaluate |F.n do where F(x,y,z)=(x² +cos yz, y – e" ,z² +x*) and S is…

A: According to question given :F(x,y,z)=x2+cos yz, y-ez, z2+x2S is the boundary of the solidBounded by…

Q: Use the Divergence Theorem to evaluate F. ÑdS where F(x, y, z)=x²i +2y²j+z²k S and the surface S is…

A:

Q: 53. Verify the divergence theorem for A = 2x?y i – y² j + 4xz2 k taken over the region in the first…

A: Given : A=2x2y i- y2j + 4xz2 kbounded by y2+z2=9 and x=2

Q: 7. Use the divergence theorem to find the outward flux of F= 3xy²i+ xe² j+ z° k across the boundary…

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Q: Use Gauss' Divergent Theorem to calculate F. dS where F = (2x + sen (et1)) i+3y²j+ cos(z²)k and S is…

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Q: 5. Use the Divergence theorem to calculate the z = 4 - x- flux of F across S where -x² + y? = 9 F =…

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Q: Use the Divergence Theorem to evaluate Double intergal Z Z of S  −→F . d−→S Where −→F (x, y, z) =…

A: Given that, F=3xy2i^+xezj^+z3k^ and the surface S:y2+z2=1,x=-1,x=3

Q: b) Use the Gauss-divergence Theorem to find the surface integral ff, F.n ds, where S is cylinder x²…

A: As stated in question we will use Gauss-divergence Theorem to solve this question.

Q: 12/ Vse the divergence theorem to evalvate the flux ef the fleld FC,22= a (3yt sin l2),9z+?+9y²…

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Q: Verify Green's theorem in the plane for (3x² -8y²)dx+(4y-6xy)dy, where C is the closed curve of the…

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