39.) The solid bounded by the cylinder x+y² = 9 and the planes z= 0 and z = 3 - x. 40

Q: 1. The solid in the first octant bounded by the coordinate planes and the surface z = 1- y – x2.

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Q: 1. A solid G is bounded by the paraboloid z = 4 – x² – y², the cylinder x² + y? = 4 and the plane z…

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Q: 8.Evaluate the triple Integral. Te by The paraboloid X=2yt + 2z? and the plane X=2. 7x dV, where E…

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Q: 1) Find the vdlemes of the oolids generated by revolving the resion in the first quuadrant bounded…

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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: 5. . Find sSSzdv where D is the 2 solid bounded by xty'tz=4 and 2= 13x²+ 3y2. (" sce Cueam Come')

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Q: And the Vorume of the solid gererated by rovolung the reglon boundid by the given ines't (urves…

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Q: If F= 2y I- 3J +x²k and s the surface parabolic cylinder y= 8x in bounded by the planes OF the 2.…

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Q: The solid bounded by the surfaces: S1 : −2(z − 2) = y2 S2 : z = (x−1)/2 S3 : x = 0 S4 : y = 0 S5 :…

A: Given surfaces are S1: -2(z-2)=y2S2: z=x-12S3:x=0S4:y=0S5:z=0 Given figure is since, solid is in…

Q: 2) Use a change of variables to evaluate ff, zdV; where D is bounded by the paraboloid z = 16 – x² –…

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Q: 4. Finl the volume bounded by the surfaces z x2 and z 4-x2-y2.

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Q: 2. The solid outside the cylinder x² + y² = 1 that is bounded above by the sphere x² + y? + x? = 8…

A: The solution is given below

Q: 3. Find the olume of the solid generated by revolving about the line z--4 the region bounded by that…

A: Here is the solution of the given problem

Q: - The region bounded by y = 2 -x, y = 0, x = 1, x = 2 is rotated about the x axis. 197/12

A: volume generated by revolution of the solid is 19π12 detailed solution with explanation is given…

Q: The solid bounded by x = y? – 1, z = 1 – y², z = 4 – x, and z = 0.

A: Given that,

Q: 5. If F=2xi - xj + y*k, evaluate ffLF av over the region bounded by the surfaces x = 0, y = 0, y = 6…

A: Given: F→=2xzi∧-xj∧+y2k∧region bounded by the surface x=0,y=0,y=6 and z=x2 ,z=4

Q: Evaluate the triple integral edV where E is bounded by the parabolic cylinder z = 1 - y² and the…

A: Given ∭x8ey dV

Q: A solid G is bounded by the paraboloid z = 4 – x2 – y², the cylinder 22 + y? = 4 and the plane z =…

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Q: (2) Find the integral (0,2,0) and (0,0,1). where D is the tetrahedron with vertices (0,0,0),…

A: Given : ∬∫x+2y+z dV             where D is  tetrahedron with vertices 0 ,0 ,0  , 1 , 0 , 0  , 0, 2 ,…

Q: 4. Find each volume. (a) A solid is being bounded by paraboloids z = 2x² + y? and z = 27 – x² – 2y?.…

A: We have to find the volume  from the given condition

Q: 2. Find the area of the plane region bounded by y = 3x + 1, x = 1, x = 3,and the x-axis. y y = 3x +…

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Q: Considering f(, Y, z) = z + x²y and S as part of the cylinder y² + z² = 25 that is between the plans…

A: It is given that surface S is the part of the cylinder y2+z2=25 lies between the planes x = 0 and x…

Q: 4. Find the volume of the solid generated when the region bounded X - 2 by f(x) = x = 1, and the…

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Q: Let S be the portion of the cylinder z = 1 − x2, in the first octant and between the planes y = 0…

A: We will find out the required value of a.

Q: 3. The solid bounded by z = 0, z = 1 – x², z = y and 2y + z = 12.

A: Given that  Region z=0,z=1-x^2 and 2y+z=12  To form a triple integral

Q: 15.) The solid in the first octant bounded by the coordinate planes and the plane 3x + 6y + 4z = 12.…

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Q: 5. Set up an iterated triple integral in the order dxdzdy that gives the volume of the solid in the…

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Q: Use Green's Theorem to evaluate the line integral (y – x) dx + (2x – y) dy for the given path. = x²…

A: Green's Theorem: By Green's Theorem we have for a differentiable function f(x,y)=M(x,y)+N(x,y) and a…

Q: 2 2 5. Find the volume of the solid bounded by the surface f (x, y) = 3x´y´ and the curves y = 2x -…

A: We will have to find the volume of the solid bounded by the surface f(x,y)=3x2y2 and the curves…

Q: Compute (ax + by² + cz) dS over the sphere x +y +z² = 1.

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Q: The solid in the first octant bounded by the coordinate planes, y+ z = 4, and x = y.

A: The objective is to find the volume for y+z=4,x=y The volume of the integral formula is,…

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

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Q: Show that 1 y - X 1. Z-y X-Z = 1. %3D alx-y) alz - x)

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Q: Sketch the solid described by the given inequalities. 0srs 8, -T/2 se S T/2, 0szs 1. 1.0 1.0 z05…

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Q: The solid bounded by z = x, z = 2 – x², z + y = 3, and y = 0

A: Volume of a solid is obtained using triple integration by the formulae =∫∫∫dx dy dz The solid is…

Q: 9. The solid bounded by x = 1 – y?, z = y², x = 5, and z = 9.

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Q: 5. Evaluate z dV, where E is bounded by the cylinder y? + z2 = 9 and the planes x = 0, y = 3x, and z…

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Q: 3. Determine the valume of the solid ebtained by rotating the region bounded by y=x² and x =y2 about…

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Q: 2. Find the surface area of the solid generated by rotating the region bounded by the graphs of f(x)…

A: In this question we have to find the surface are of the solid region generated by rotating the…

Q: 15. The solid enclosed by the sphere x2+ y2 + z2 = 4a? and the planes z = 0 and z = a. %3D

A: Given: x2+y2+z2=4a2          ... (1) z=0z=a

Q: 2. Evaluate , dV, where o= 45 x²y and V is the closed region bounded by the planes 4x + 2y +:=8, x=…

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Q: 6. Consider the solid Q bounded by the surfaces S1 : 1 = 4 – 22 S2 : 1+y = 5 S3 : 1 = 0 S4 : y = 0…

A: Solid bounded by surfaces: Double integration can be used to find the volume of a solid limited by…

Q: 4. Evaluate x²dV G where G is a solid that lies in the first octant bounded by x? + y? = 3z and z =…

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Q: 4. Set up an iterated double integral equal to the volume of the solid in the first octant bounded…

A: The region is

Q: 2. Find the volune og the solid gonned by revohing abaut thie lere y y=4x+1, y: -1 bounded by 4x +3,…

A: The volume for solid of revolution generated by revolving the area bounded by curves y=f(x) and…

Q: 3.4.6 Evaluate the line integral [sin y dx + (x- cos y) dy] taken in the anticlockwise sense, where…

A: Green's Theorem States that  Let C be the positively oriented, smooth, and simple closed curve in a…

Q: 10. The solid bounded by y = 4, y – x = 1, z = x², and z = = 4.

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Q: Find ¹JJ²₁ z dV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,2,0), and…

A: The solid E is the tetrahedron with vertices 0, 0, 0, 3, 0,0, 0, 2,0 and 0, 0, 1. Draw the solid E:…

Q: 2. The solid in the first octant bounded by the planes x = 0, y = 0, z = 1, z = 2 – y, and the…

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