(22. //I (a² + y²) dV where E is the solid that lies between 2 spheres x² + y? + z2 = 4 and a? + y² + z² = 9 (1) Evaluate

Q: xxS y dS S is the part of the paraboloid y= x 2 + z2 that lies inside the cylinder x 2 + z2 =4

A: And the projection of S onto the xz-plane is given by the disk So using the parameterization in x…

Q: 1. Calculate the integral 1 y-stnx)dx + cosy dy a) With directly (classical), b) With the Green's…

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

Q: Solve the triple integral " (x²+ y²)-1/2dzdydx by changing to cylindrical coordinates 0. 0. O 9/3n O…

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Q: 46.) (a) Parameterize S the 1st octant portion of the cylinder y² + z² = 9, 0 <x<4 (b) Use above to…

A: y2+z2  0≤x≤4x=uy=3 cos vz=3 sin vparameterise the surface ass(u,v)=(u   3 cos v   3 sin v)0≤u≤4,…

Q: (9) Evaluate // 2² + y² + z²)³/? dV where D is the solid region in the first octant between the two…

A: Volume between the two spheres using spherical coordinates

Q: II| (x + y + z) dv, where E is the solid in the first octant that lies under the paraboloid z = 16 -…

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Q: 19. Evaluate II \xyz| dx dy dz over the solid ellipsoid x² y2 < 1. a? (Hint: Let x = au, y = bv, and…

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Q: 3. Evaluate // (22 + y) dV where G is the solid in the first octant bounded by r = y? and r+z = 1.

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Q: 1 Evaluate dV, where E lies between the spheres a? + y? + z? = 16 and x2 + y2 + z2 = 64 in the first…

A: The region E lies between the spheres: x2+y2+z2=16  and  x2+y2+z2=64  in first octant.

Q: The surface area of the surface generated by revolving y= 1 – x² for 0<x<1 about the x – axis is s=…

A: The solution is as follows

Q: The surface area of the surface generated by revolving y=1-x? for 0<x<1 about the x- axis is None s=…

A: surface area S =∫012πy.ds where ds=1+(dy/dx)2

Q: 4. If the curve y = In x between x = 1 and x = e is rotated about the y axis, which integral below…

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Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = E : 6y² + 6z²…

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Q: 2. Show that the surface area of the solid of revolution obtained by revolving the curve y = 1/x, x…

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Q: T// Vx² + y² dV, where E is the solid in R3 bounded by the surfaces E z = x² + y² and z = 8 – x² –…

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Q: The surface area of the surface generated by revolving y=1-x² for 0<x<1 about the x- axis is s=…

A: If you like the solution then please give it a thumbs up.... The Answer is:              S =…

Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = 9y² + 9z2 and x…

A: Given the region

Q: 10. Let D be the solid inside the cylinder r= cos , above the xy-plane and under the paraboloid…

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Q: (10) Find the work done by F = -yi+ xj+ zk on a particle moving along the helix r(t) = where 0 < t <…

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Q: 3) Evaluate the cylindrical coordinate integrals in: 2n 1 1/2 ISPsin'e + z") dz r dr de e-1/2

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Q: (1) Sketch the regions of integration. (a) 3m/2 (b) (r,0)r drdo 3m/4

A: The integrations  (a). ∫-π2π2∫04f(r,θ)rdrdθ(b). ∫3π43π2∫34f(r,θ)rdrdθ We have to sketch the regions…

Q: 5. Evaluate Sl. x2 dV where is the solid that lies within the cylinder x² + y² = 4 above the plane z…

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

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Q: ¹ [ ] [ ²0 x dxdydz where E is the solid limited by Plane E z = 0,z=x+y+5 and by the cylinders x² +…

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Q: 5. On the surface z-3x^2+2y^2 (an elliptic paraboloid), (x,y) changes from (1,1) to (0.99,1.02). Use…

A: Since you have asked multiple questions, we will solve the first question (Question 5) for you. If…

Q: Given o V4-r2 4-r2-y2 -2-V4-12 x dzdydx 0. Choose the correct triple integrals in cylindrical…

A: Given

Q: The integral JJI eV 4x2 + 4y² + 4z² dV = mt, where R is the solid hemisphere with x2 + y? + z² < 11…

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Q: - Evaluate the integral 4-z²-y² 1 dz dy dx Jo 4-z²-y² x² + y² + 2² using spherical coordinates.

A: To evaluate ∫-22∫04-x2∫-4-x2-y24-x2-y2 1x2+y2+z2 dzdydx

Q: y? = 1? Which of the following integrals represents the length of the upper half of the ellipse 25…

A: Topic = Application of integration  Correct answer = A

Q: The surface area of the solid of revolution generated by rotating x = (y² + 2)²,1 < y s 2 about the…

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Q: (15) Evaluate ///, y dV where D is the solid cut from the cylinder 2² + y? = 1 by the planes z = 0…

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

Q: 1. Evaluate ſf, y dS where S is the portion of the cylinder 4x² + 2y² = 16 that lies between z = 0…

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

Q: Evaluate II| 6x(x2 + y2) dv, where E is the solid in the first octant that lies beneath the…

A: Since the integral lies in first octant so 0≤θ≤π/2 and z≥0.  Converting into cylindrical coordinates…

Q: Evaluate 1 dv √x² + G where G is a solid that lies inside the cylinder x² + (y − 2)² = 4, above the…

A: Please see the attachment

Q: Evaluate /|/ (x² + y² + z²)² dV where E is the solid ball centered at the origin with radius 2.

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Q: 22. Evaluate xyz dV, where E lies between the spheres p - 2 and p- 4 and above the cone - 7/3.

A: Solution:-

Q: 3) Evaluate the cylindrical coordinate integrals in: 2n 1 1/2 || | (r²sin²0 +z²) dz r dr d0 0 0 -1/2

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Q: 27) If the solid of revolution formed by rotating R2 about the y-axis is a cylindrical shell, then…

A: You have posted multiple questions. As per the instruction, we will be answering only the first one…

Q: No. Date Evaluate fff dv G x² + y² where G is a solid that lies inside cylinder *+(4-2)² =4 obove…

A: we will use cylindrical co ordinate system to solve the given integral

Q: 1. Evaluate ſſ, y dS where S is the portion of the cylinder 4x² + 2y² = 16 %3D that lies between z =…

A: Given S is portion of cylinder 4x2+2y2=16 that lies between z=0 and z=7. Parametrize the surface s.…

Q: =+ x²y) ds part of the cylinder y² + z² = 9 that lies between the planes x = 0 and x = 3 in the…

A: See the details solution in below

Q: The surface area of the surface generated by revolving y 1-x? for 0Sr<1 about the x-axis is S=…

A: Rule- If the curve y=f(x), a≤x≤b is rotated about the x−axis, then the surface area is given by

Q: 1 Use Cartesian coordinates to evaluate [[[ y² dV where D is the tetrahedron in the first octant…

A: We have to find the volume of the solid and Draw Solid.

Q: 8. Evaluate x dV where E is the solid enclosed by the paraboloid r = y²+2? and the plane x = 9

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Q: 1 Evaluate dV, where E lies between the spheres a? + y? + z² = 16 and E x2 + y? + z2 x? + y? + z?=…

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Q: Consider the solid Q shown in the following figure 2.x + 3y + 3z = 6 S y? + x = 2 2 If S: 2x + 3y +…

A: The given surface is as follows: 2x+3y+3z=63z=6-2x-3yz=136-2x-3yz=2-23x-y The projection of the…

Q: 1. Evaluate the line integral I = = [v¢4x° + y*) dx + x(2x° + 3y*) dy] around the ellipse x/a? +…

A: The given line integral is, I=∮y4x2+y2dx+x2x2+3y2dy We know the Green's theorem:…

Q: The volume of the solid generated by the curve y = e¯ª, between x = 2 and x = 7 about the x – axis…

A: Given curve, y=e-x x=2  and   x=7

Q: 1. Evaluate using cylindrical form, I. yz dV where S is the solid in the first octant enclosed by y…

A: Given : y = 0 and y = 1-x2 and z = x To find : Area enclosed by given solid. Solution : The…