10. Let S be the surface of the solid bounded by the paraboloid z= the plane z=4 as in the picture. Assume the orientation of S is positive. Let 2+y and F = -yzi+ (y + cos(z²))j+ zy°k. Compute the surface integral SP· A by using Divergence Theorem. of

Q: 1. The solid bounded by y = 1, y = x², z = 0 and z = y AS A Z-SIMPLE SOLID.

A: Givne that  Solid region y=1,y=x^2,z=0 and z=y  To find the triple integral

Q: 3.4.8 Evaluate the surface integral ff, U(x, y, z) dS, where S is the surface of the paraboloid z =…

A:

Q: 2. Let D = 2xyā, + 2(x² + z²)d, + 4yzd, C/m² and evaluate surface integrals to find total charge…

A: given D→=2xy ax→+2x2+z2 ay→+4yz az→ it is known that ρ=∇·D→ it is known that…

Q: Q3// A surface S is defined by 2x2 + 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. ) ر م(ل 2) ds S is the part of the cylinder x² + y2 = 16 that lies…

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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: 5. (a) Evaluate the surface integral /3² dS where o is part of the cone z = VT + y² that lies…

A: As you post multiple questions According to the guideline I only solve the first problem please post…

Q: . Evaluate (x² + y) dv G if G is the solid bounded by the parabolic cylinder z = y², xy-plane and…

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Q: 1 : : Evaluate F dS whereF = (r",y",) and S is the solid bounded by the ry plane and the elliptic…

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Q: 5. Evaluate the surface integral S_(x+ y) ds ; o is the part of the plane 2x + y +z = 3 that lies in…

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Q: Find the Volume 6t prime bounded Parabolid ( top Surface) z = x'+y regi on in M=2y, ソ=o the by the…

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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: Evaluate the surface integral. z + x2y x²y) ds S is the part of the cylinder y² + z2 = 9 that lies…

A: We have to find the surface integral from the given condition

Q: 13. Calculate the flux of F across S.F = (3x, xz, z2) and S is the surface bounded by the paraboloid…

A: Given vector field is  F=3x,xz,z2 we have to find the flux through F where S is the surface bounded…

Q: Evaluate /// 203 dV G if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: Here we have to find range of values for x,y and z and then find triple integral

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: Use cylindrical coordinates to evaluate the triple integral □ لاا √² + y²dV, where E is the solid…

A:

Q: 4. Let S be the portion of the paraboloid z = 4 – x² – y? in the first octant. (a) Evaluate the…

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Q: 1. Find the volume of the solid bounded by the paraboloids z = 6 – x² – y² and z = 2x² + 2y².Use…

A: From the given problem:   z=6-x2-y2  ; z=2x2+2y2   For finding volume we using the triple…

Q: 5. Use our Early Parameterization step by step including sketch of the surface to evaluate the…

A: Given that The equation of cylinder in the xz-plane as x2+z2=1 Also, the given surface integral lies…

Q: (9) Evaluate the surface integral / S, czdS, where o is the part of the plane r+2y+3z = 6 that lies…

A:

Q: Evaluate the surface integral. z2 dS, S is the part of the paraboloid  x = y2 + z2  given by  0 ≤…

A: given the surface integral  z2 dS  where S is the part of the paraboloid x= y2+z2   given by 0≤x≤1…

Q: 1. Find the volume of the solid bounded by the paraboloids z = 6- x² - y and z = 2x? + 2y2.Use polar…

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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…

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Q: Verify the Green's theorem for integral x²y dx + xy dy, where C is the boundary described…

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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: Evaluate SſF-dš where F = yi +2x j +(z-8)k and S is the surface of the solid bounded by 4x + 2y +z =…

A: By using the divergence theorem we solve the above question

Q: 6. Below is the solid bounded by the surfaces S1:z° = 16 – 2y S2: x = 4-y + z, S3: x = 1, in the…

A: Given a solid described by,  s1:z2=16-2ys2:x=4-y+zs3:x=1.

Q: 9. If F = (x – z) î + (x³ + yz)ĵ + 3xy² k and S is the surface of the cone z = a – Va? +y?) above…

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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: Evaluate the surface integral. (z + x2y) ds S is the part of the cylinder y2 + z2 = 16 that lies…

A: Given ∫∫S(z+x2y)dS where S is the part of the cylinder y2+z2=16 that lies between the planes x=0 and…

Q: Let S be part of the outward-oriented hyperboloid of one sheet x² + y² = z² = 1 that lies within the…

A: Given x2+y2-z2=1 and x2+y2+z2=3

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: 1) Consider the solid Q in the first octant, generat surfaces: z = (y – 3)² + 1, 2r + 4z = 16, 1= 1,…

A: Volume of solid: Let z=f(x, y) and z=g(x, y) be the functions of x and y of a solid, and let x=a to…

Q: 15. Evaluate SLL:(z+1)dV where E is the solid enclosed by the paraboloid y = x2 + z² and the plane y…

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Q: Evaluate the triple integral. SSS 5x²e" dv I where E is bounded by the parabolic cylinder z = 1 - y²…

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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: (a) Compute the surface integral || a xy dS, where S is the quarter cylinder x2 + y? = 1; x, y > 0…

A: Given that The surface integral is ∬Sxy dS, where S is the quarter cylinder x2+y2=1; x,y≥0 between…

Q: Evaluate the surface integral. JI (12 + y2 + 2) ds S is the part of the cylinder x2 + y2 = 9 that…

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Q: E) Sketch the solid bounded by the cylinder ** +y = 4 and the planes y+z = 4 and z = 0

A: Here, we need to sketch the solid bounded by the cylinder x2+y2=4 and the planes y+z=4 and z=0.

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

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Q: Evaluate (x² + y) dv G if G is the solid bounded by the parabolic cylinder z = the planes x = 0, x =…

A: Here I am using simple tripple integration to solve this question.

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: 5. Use the Divergence Theorem to calculate the surface integral Ss F dS, where F(r, y, 2) = r'i+…

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Q: Let the surface Σ be the solid bounded by the paraboloid z “ 1 ´ x2 ´ y2 and the xy´plane.…

A: Use Gauss divergence theorem to compute the outward flux.

Q: 1. Use the cylindrical coordinate to evaluate fll. x² + y²dV where G is the solid bounded by…

A:

Q: 1. Evaluate the surface integral SL xz² ds ; o is the part of the cone z = Vx2 + y² that lies…

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Q: Use Stokes’ Theorem to evaluate F(x, y, z) = 3zi + 4x j + 2yk; C is the boundary of the paraboloid…

A: Use Stokes theorem

Q: 4. Evaluate S. F di where F(x, y, z) = (x – y²)i+ (y – z²)j+ (z – x²)k and C is positively oriented…

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Q: 3. Evaluate the triple integral || ryz dV; G is the solid in the first octant that is bounded by the…

A: To evaluate the given integral ∫∫∫Gxyz dV. The limits are given as  z=0 to z=2-x2 and y=0 to y=x and…