1 9. Evaluate dV;where E is the solid between the spheres of radius 1 (x² + y² + z²)³/2 E and 2 centered at the origin

Q: (3) Find The solution of the intigl uglue pablem y(-e) =0 %D (2 none of the given answels (3 %3D %3D…

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Q: 1 Evaluate E 22 + y² + z² dV, where E lies between the spheres a? + y? + z² = 16 ar ² + y² + z² = 25…

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Q: 13 - x² – y? at (3, 2, 0), then If the point (1, 1, k) lies on the tangent plane to the paraboloid z…

A: z=13-x2-y2 Partially differentiating with respect to x, we get zx=0-2x-0=-2x Partially…

Q: 1. Use Green's theorem in order to compute the line integral $ (3cos + 6y?) dx + (sin(5") + 16x³) dy…

A: Here the given integral is                               ∮C3cosx+6y2dx + sin5y+16x3dy

Q: Example 1 Evaluate [[[16z dV where E is the upper half of the sphere x² + y² +z? =1. Solution Since…

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Q: Question 15 Evaluate f S f6zdV E where E is the solid enclosed by z = 1 and z = x ² + y? O 27 47T…

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Q: QUESTION 8 Find the area of the cylindrical surface in Xyz-space where a point (X,y,z) on the…

A: Find the surface area of the cylinder in xyz-space where a point x, y, z on the surface satisfies…

Q: 14 13 12 11 10 9 8 7 4- 3- 2- Find the volume of the solid S obtained by rotating R about the line y…

A: Here R is the region bounded by y=9x,x=2.5 and the x-axis i.e.(y=0)and the solid…

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: 1. a) Use the cylindrical coordinates to evaluate (3 + xy)dV, where E is the solid E in the first…

A: Here is the solution of the given problem.

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: U SIII u' cos u?, EXAMPLE 6.6.3 For a surface of revolution defined by x u! oin o? COS 3 flol) aub…

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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: 6. Determine the volume V of the 3 dimensional lampshade formed (see diagram below) by rotating the…

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Q: 1. Evaluate SSSE z dV where E lies between the spheres x2 + y? + 2² = 1 and a? + y² + z² = 4 in the…

A: Given, ∫∫∫EzdV where E lies between the spheres x2+y2+z2=1 and x2+y2+z2=4 in the first octant.

Q: 12. Consider the lamina covering the regon x442-2,0EXET WH aunsity functionplx,u) = - 5x + 2u+5. 1ts…

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Q: 1.3. Derive the mass conservation statement for spherical coordinates [eq. (1.10)] by writing eq.…

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

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Q: | eョで)) dV=

A: Given:              ∭Dex2+y2+z232dv        d is the region in the first octant between spheres…

Q: Solve the following initial and boundary problems Luz + (4x – 1) uy = 0 (a) и (0, у) — Im y. { %3D

A: We have to solve the given initial and boundary problems.…

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

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Q: 10.18. Use an appropriate change of variables to evaluate the integral ff,(1 + x? + y²)²dA, where T…

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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: .... ........ 4.8. Find the area of the surface generated by revolving the curve x = cost, y =…

A: See the details solution in below

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: The shape of a redwood tree (without any branches) can be modeled by an upside down paraboloid, f(x,…

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Q: 5. Use Cartesian coordinates to evaluate If y² dv where D is the tetrahedron in the first octant…

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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: 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: 1 I. Evaluate dV, where E lies between the spheres x? + y² + z² = 1 and x2 + y? + z² E x2 + y? + z?…

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Q: 3. If E = 12ay at origin due to infinite surface charge located at (а) х > 0 (b) z>0 (с) у <0 (d) z…

A: The electric field due to infinite surface charge density σ is Eσ  Electric field at a point is…

Q: 1.Let 3 le the solid obtained by rotating by region shown in the fiqure about the Assume as3 and b=…

A: Given: y=ax(x-b)2 and y=0 and  0≤x≤b The rotation about the y-axis. Assume a=3 and b=1

Q: 3/5ketch, E Valuate & reverse the order of in tegration 2. ol X dy

A: We are looking at the following curves simultaneously: y = ex y = 1 x = 0 x = 2

Q: 1. Evaluate the integral |// cos (-) dV, where G is the solid defined by the G inequalities <y< , y…

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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: y = cos(x), 0 <x<

A: Consider the given surface whose area is required to calculate.

Q: 1. Evaluate the integral: SSS, x² + y² + z² dV where D lies above the cone z = spheres x? + y? + z²…

A: Here we have to evaluate the integral value, where D lies above the cone z= √(x2+y2) and between the…

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: 3. Solve the Laplace equation inside a 60° wedge of radius 1 subjected to the boundary conditions…

A: The Laplace equation is given by: r2∂2u∂r2+r∂u∂r+∂2u∂θ2=0 The boundary conditions are: ∂u∂θr,0=0,…

Q: Example 6: Evaluate ez dz dy dx E Where E is enclosed by the paraboloid Z = 3+ x? + y² , the…

A: The given problem is to evaluate the given triple integral of given function ez for which region E…

Q: 7. Evaluate the integral I | sin(9.r² + 4y²)dA by hand, using an appropriate change of variables,…

A: The given question can be solved as shown in step2

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: Obtain the Solution x, y > 0, xy > 1 of the PDE 2y on the x+y 1 Uxy such that u = x+y 0, ux…

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Q: ³ SS ²0 Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,6,0), an

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