5. Compute / | F. aš, where F = (y, -x, 2z) and S is the surface of the sphere of radius 2, centered at the origin, and given the positive outward orientation, by applying the divergence theorem.

Q: 15. If the surface S has projection R on the xy-plane, show that F.īdS = S da dy ה.F provided |ñ -…

A: Question: If the surface S has projection R on the xy-plane, show that ∬SF¯·n¯dS=∬RF¯·n¯dxdyn¯·k¯…

Q: Q19// A scalar filed V = xyz exists over a surface S defined by %3D x2 + y2 9 bounded by the plane…

A: given scalar field V=xyz exists over a surface defined by x2+y2=9 bounded by the plane x=0,y=0, z=0…

Q: 1. Use the Divergence Theorem to evaluate F.dS where F (3z – za) i+(- 1) j+ (4y +) k and S is the…

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Q: Q2// A surface S is defined by x2 + z = 9 and the bounded by the planes y = 0, y = 1,x = 0,z = 0 in…

A: Given that V=xy2z And y=0, y=1,x=0,z=0 The given surface is x2+z=9 The integral formed is,…

Q: Use Divergence Theorem to evaluate ,0i +rj +ryh) ds, Q#3(a) where S is the upper part of the sphere…

A: As per bartleby instruction when more then one question is given only one has to be answered. Please…

Q: Evaluate both sides of divergence theorem for A = pa,+pcos(@)a , + za , through the closed surface…

A: Given vector field is  Divergence theorem

Q: 2. Use the Divergence Theorem to evaluate F.dS where F = 4x i + (1 – 6y) j +k and S is the surface…

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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: use the Divergence Theorem to find the outward flux of F across the boundary of the region F = x2i -…

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

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Q: * Use the Divergence theorem to find , F. dS where F(z, y, z) = (zy, y, -zy) and S is closed surface…

A: Using surface integral, answer is 8π

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 the line integral / x°z ds, where C is the line segment from (0, 2,4) to

A: Line integral: - The function to be integrated is determined along a curve in the coordinate system…

Q: Let F= [x, y, z] and S be a sphere of radius R. Using the divergence theorem, the value of the…

A: Given : F = x,y,z

Q: Evaluate the line integral xyld x + (x²+y)dy] +. where c is the saruare farmed by the lines

A: Let us consider a line integral ∫CP dx+Qdy then it can be written as  ∫D∫∂Q∂x-∂P∂y dA  Where, P and…

Q: d) An open surface F is given by F = {(x,y, z) |z = 4 – x² – y² , z > 0} . Compute the flux of V…

A: V(x,y,z) = <2x+3y,2y+3x,-4z>F={ (x,y,z) : z=4-x2-y2 , z≥0}Consider, g(x,y,z) = z+x2+y2-4…

Q: |s, is calculated by the thorem of divergence of the full range straight flux F(x, y, z) = 2xỉ + yj…

A: Answer  Flux = 2π

Q: 5) S, is calculated by the thorem of divergence of the full range straight flux F(x, y, z) = 2xi +…

A:

Q: Verify Gauss Divergence Theorem for F = (x3- yz)i+ (y² - xz)j+ (z3 – xy)k %3D taken over a…

A: GivenF→=x3-yzi^+y2-xzj^+z3-xyk^taken over a rectangular  parallelepiped bounded by 0≤x≤a,0≤y≤b and…

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: Q2// A surface S is defined by x2 + z = 9 and the bounded by the planes y = 0, y = 1,x = 0,z = 0 in…

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: 8. Use Green's Theorem to calculate f, x?y³dx + (xy - y?)dy where C is the boundary of the region…

A: The given integral is ∫Cx2y3dx+xy-y2dy, where C is the boundary of the region lying between the…

Q: Evaluate both sides of divergence theorem for A = pa, + pcos()a,+ za, through the closed surface…

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

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Q: 5) S, is calculated by the thorem of divergence of the full range straight flux F(x, y, z) = 2xỉ +…

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Q: State what the Divergence Theorem says, using your own words. You may assume that E is a solid in R³…

A: We can state the Divergence theorem .

Q: Evaluate both sides of divergence theorem for A = pa, + pcos()a , + za, through the closed surface…

A:

Q: Use the Green's Theorem to evaluate the line integral 2xydx + x² – y² dy where C is the curve…

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Q: 5/ MATH

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Q: Evaluate both sides of divergence theorem for A= pa,+ pcos()a+ za, through the closed surface…

A:

Q: 5) S, is calculated by the thorem of divergence of the full range straight flux F(x, y,z) = 2xi + yj…

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Q: evaluate.both sides of divergence theorem for A= ra,+rcos(e)a, +ra, through the closed surface…

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Q: Evaluate both sides of divergence theorem for A = pa, + pcos(ø)a, + za, through the closed surface…

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Q: Evaluate both sides of divergence theorem for A= pa, + pcos(6)a+za, through the closed surface 0<p<…

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

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Q: Evaluate both sides of divergence theorem for A = pa, + pcos($)a+za, through the closed surface…

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Q: Evaluate both sides of divergence theorem for A = pa,+ pcos(ø)a,+ zaz through the closed surface…

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Q: Given F = ryx – ỳ + zà, use the divergence theorem to evaluate f, F. dS over the closed surface…

A: Given F→=xyx^-12y2y^+zz^The closed surface consisting of the three surfacesfz=z-4+3x2+3y2when…

Q: evaluate both sides of divergence theorem for A= ra,+rcos(8)a , +r²a, through the closed surface…

A: Given problem is :

Q: Let S be the sphere of radius 2, oriented inward. Let F = (2x + e", 4y + e*, 2:2). Use the…

A: In the given question we have to solve the double integral s.t∫∫F.ds  to the help of divergence…

Q: Use the Divergence Theorem to evaluate F. dS where S is the sphere r² + y² + z² = 9 and F = (3r, 2y,…

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Q: Use the divergence theorem to evaluate Is F·N dS, where F(x, y, z) = yʻzi + y°j + xzk and S is the…

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Q: Evaluate both sides of divergence theorem for A = pa,+ pcos(o)a,+ za, through the closed surface…

A: Given A=ρaρ+ρcosϕaϕ+zaz and the closed surface is 0≤ρ≤1, 0≤ϕ≤π, 0≤z≤2. We have to evaluate the both…

Q: Use Divergence theorem to find the ouward flux of F = 2xz i - 3xy j – z2 k across the boundary of…

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Q: Evaluate both sides of divergence theorem for A= pa, + pcos(0)a , + zaz through the closed surface…

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Q: Use Divergence theorem to find the ouward flux of F = 2xz i - 3xy j – z2 k across the boundary of…

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Q: Let F(x, y, 2) = 32?ai+ (y³ + tan(z))j+ (3x²z- 4y?)k. Use the Divergence Theorem to evaluate fs F dS…

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Q: Verify the Divergence Theorem for the F(x,y,z) = 4xi +4yj +2z? k over the surface S of x² +y² and z…

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