• Solution. In cylindrical coordinates the region E is described by 0 ≤ r ≤ 1, 0 ≤ θ ≤ 2π, and 0 ≤ z ≤ 2r. Thus, ZZZ E x2 dV = Z 2π 0 Z 1 0 Z 2r 0 (r cosθ)2 rdzdrdθ = Z 2π 0 cos2 θdθ Z 1 0 2r4 dr = 2π 5. 4. Use spherical coordinates in the following problems. (a) Evaluate RRR E xe(x2 +y2 z2)2 dV , where E is the solid that ...
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  • it type of feels which comprise you're meant to be doing a triple needed (which simplifies to a double needed) you blend from z= 2+x^2+(y-2)^2 to z=a million interior the z direction. This in basic terms resources the function 2+x^2+(y-2)^2 - a million = a million+x^2+(y-2)^2 then you definitely evaluate the double needed of one million+x^2+(y ...
  • Find the volume of solid S that is bounded by elliptic paraboloid x^2+2y^2+z=16, planes x=2 and y=2 and the three coordinate planes. Show the volume graphically.
  • Use cylindrical coordinates. find the volume of the solid that is enclosed by the cone z = x2 + y2 and the sphere x2 + y2 + z2 = 72. 1 See answer quirasams7749 is waiting for your help. Add your answer and earn points. LammettHash LammettHash Let be the solid. Then the volume is
  • Answer to: Use cylindrical coordinates. Find the volume of the solid that is enclosed by the cone z = sqrt(x^2 + y^2) and the sphere x^2 + y^2 +...
  • Problem 2: Find the appropriate limits for integrating over the region bounded by the paraboloids z = 3x2 + 4y2 and z = 9 x2 5y2. Check your results using viewSolid. What is special about the examples we have just considered is that the region in question is bounded by two surfaces, each of which has an equation specifying z as a function of x ...
  • MATH 2004 Homework Solution Han-Bom Moon 15.3.36Find the volume of the solid by subtracting two volumes, where the solid is enclosed by the parabolic cylinder y = x2 and the planes z = 3y, z = 2+y. Two planes meet over 3y = 2+y ,y = 1.

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Use polar coordinates to find the volume solid under the paraboloid z = x2 + y2 and above the disk x2 + y2 9 40.5 pi -7.5 pi 68.5 pi 140.5 pi -43.5 pi solid bounded by the paraboloid z = 7 - 6x2 - 6y2 and the plane z = 1. 13 pi 6 pi 4.5 pi 2 pi 3 pi solid under the paraboloid z = x2 + y2 and above the disk x2 + y2 49.
MATH 2004 Homework Solution Han-Bom Moon 15.3.36Find the volume of the solid by subtracting two volumes, where the solid is enclosed by the parabolic cylinder y = x2 and the planes z = 3y, z = 2+y. Two planes meet over 3y = 2+y ,y = 1.

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Find the volume of the region bounded above by the paraboloid z = 8-x 2-y 2, bounded below by the paraboloid z = x 2 + y 2, and with y ≥ 0. In cylindrical coordinates, the upper paraboloid becomes z = 8-r 2, and the lower paraboloid becomes z = r 2. These intersect when 8-r 2 = r 2, which we solve to find r 2 = 4.

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How to solve: 1. Find the volume of the region E bounded by the paraboloids z = x^2 + y^2 and z = 36 - 8 x^2 - 8 y^2. 2. Find the centroid of E...
4. Find the volume of the solid lying under the circular paraboloid z= x 2+ y and above the rectangle R= [ 2;2] [ 3;3]. Z 2 3 Z 2 2 x2 + y2 dxdy= Z 3 3 1 3 x3 + y2x x=2 x= 2 dy = Z 3 3 8 3 + 2y2 (8 3 2y2)dy = Z 3 3 16 3 + 4y2 dy= 16 3 y+ 4 3 y3 3 3 = 16 + 36 ( 16 36) = 104 5. Find the volume of the solid under the paraboloid z= 3x 2+y and above ...