Let D be the region in space enclosed by z = -2x² – y² and z = -12 + x? + 2y2. Our aim is to find the volume of D using triple integral in Cartesian coordinates. By using the order dzdxdy, the limits of integration of z are: -12 + x? + 2y?

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Q: Let D be the region in space enclosed by z =-2x2 - y2 and z = -12 +x2 + 2y2. Our aim is to find the…

A: To find limit for triple integral  graph of the region is always helpful .

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Q: Let D be the region in space enclosed by z = -2x² – y² and z = -12 + x? + 2y². Our aim is to find…

A: The given problem is to find the limits of the integration of z for to find the volume of given…

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A: Solution is given below:

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A: We will find out the required value.

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Q: Use the Disk/Washer method to set up the integral that computes the volume of the solid created by…

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A: We have to find the volume of the solid.

Q: Let R be the shaded region defined and bounded by the graphs of C;:y = v25 – x², C2:y =- 5, and C3:y…

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Q: Let R be the region enclosed by f(x) = x² + 2, g(x) = (x – 5)² and the axes x = 0 and y = 0. Compute…

A: Consider the given two curve.

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Q: Set up but do not evaluate the integral used to find the volume of the solid generated by revolving…

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Q: Let R be the region enclosed by f(x) = x² + 4, g(x) = (x – 3)² and the axes x = 0 and y = 0. Compute…

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Q: Set up but do not evaluate an integral to determine the volume of a solid whose base is the region…

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Q: Let f (x) = 7x and g(x) = x2 + 4x, and let R be the bounded region between the graphs of f and g.…

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Q: Let D be the region bounded below by the cone z = √(x2 + y2)and above by the paraboloid z = 2 - x2 -…

A: Given Cone is z=x2+y2   ....1 and paraboloid is z=2-x2-y2  .....2

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Q: Let D be the region bounded by the paraboloid z = x2 + y2 and the plane z = 2y. Write triple…

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Q: Let D be the region bounded below by the XY – Plane, on the side by 2 cos 0, and on top by the…

A: The general form of the volume is given as:

Q: 3. Use the shell method to set up the integral that gives the volume of the solid generated by…

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Q: 5. Let S be the solid in the first octant bounded by the cylinders x² + y? = 4 and x² + z² = 4. (b)…

A: Given- Let S be the solid in the first octant bounded by the cylinders x2+y2=4, and x2+z2=4. To…

Q: Given a solid bounded by f(x,y) = 3x² + 2y“, xy-plane, x = 3, x = 12, y = 6 and y = 16. If the order…

A: find the volume using double integration.

Q: Use a triple integral to find the volume of the solid shown in the figure. z = 36 – x2 - y² 40 30 20…

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Q: Set up but do not evaluate an integral to find the volume of the solid generated by revolving the 1.…

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Q: Let S be the solid in the first octant bounded by the cylinders x² +y² = 4 and x² + z² : -) Use…

A: The volume of the given solid S is V=∫∫∫S dVwhere solid is bounded by cylinders x2+y2=4 and…

Q: Let D be the tetrahedron in the first octant bounded by the coordinate planes and the plane 6x + 3y…

A: The volume of the region D can be calculated by the following formula. Volume=∭DdV

Q: 13. Use a double integral to find the volume of the solid bounded by the graphs of the equations z =…

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Q: Set up but do not evaluate the integral used to find the volume of the solid generated by revolving…

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Q: Assume ƒ and g are continuous, with ƒ1x2U g1x2 U 0 on 3a, b4. The region bounded by the graphs of ƒ…

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Q: Let R be the region enclosed by f(x) = x² + 4, g(x) = (x – 5)² and the axes x = 0 and y = 0. Compute…

A: Given query is to find the the volume generated.

Q: Use a triple integral to find the volume of the solid shown in the figure. z = 64 - x2 - y2 |20 60…

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A: We have to find the limit of integration of y.

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A: here we have to find the volume.

Q: Let D be the region in the plane described by all four inequalities x > 0, y x³ and y <1. Let S be…

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Q: Which one of the integrals below gives the volume of the solid region bounded by y = In x, y -2, y =…

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Q: Write the definite integral that computes the volume of the solid generated by revolving 6. the…

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Q: Let D be the region bounded by the paraboloids z = 8–x² – y² 27) (Triple Integrals) and z = x2 +y?.…

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Q: Evaluate the triple integral to find the volume of the geometry bounded by the coordinate planes and…

A: In this we have to evaluate triple integral to find volume.