12. a. Evaluate (x²+2z)dxdydz where I is the region bounded by the planes z=0 and y + z = 4 and the cylinder y = x² b. Set up a triple integral in cylindrical coordinates that gives the volume of the solid bounded above by the hemisphere z = √2-x² - y² and below by the paraboloid z = x² + y² c. Set up a triple integral in spherical coordinates that gives the volume of the solid that lies outside the cone z = √3x² +3y² and inside the hemisphere z = =√√4-x² - y².

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Q: Use spherical coordinates to evaluate the triple integral e-(z²+y²+z²) I. dV, E Væ2 + y? + 2² where…

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Q: 13. Use spherical coordinates to find the volume of the solid region Q bounded below by the upper…

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Q: Consider the part of the solid sphere x2 + y2 + z2 ≤ 4 contained in the first octant (the first…

A: I=∫∫E∫  y dvE is bounded by sphere of radius 2 in first octantusing spherical co‐ordinates

Q: Determine the area of the surface of z = x² + y² that lies below the plane z = 4. 2

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Q: Find the surface area of the piecewise smooth surface that is the boundary of the region enclosed by…

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Q: 2. Consider the solid S bounded by the following planes: a. b. 3 z = 3, z = y, z=x, and 3x + 2y - 2z…

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Q: Find the volume of the region bounded above by the paraboloid z = 4 – 3x² – 3y² and bounded below by…

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Q: the volume of the solid B that lies above the cone z = √√x² + y² and below the sphere x² + y² + z² =…

A: We will use relation between cartesian and spherical co ordinate to set up triple integral for…

Q: Use polar coordinates to find the volume inside the cone z = 2 - x² + y² and above the xy-plane.

A: Obtain the volume inside the cone z=2-x2+y2 and above the xy-plane. Find the equation of the circle…

Q: Find the surface area of the part of the plane z = 2x - y − 3 that lies inside the - cylinder x² +…

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Q: Find the surface area of the piecewise smooth surface that is the boundary of the region enclosed by…

A: Consider the given function. z=7−5x2−5y2 and z=2x2+2y2 Put the both function equal.…

Q: Use cylindrical coordinates to find the volume of the region enclosed by the cone z = + y² and the…

A:

Q: Find the volume of the solid bounded by the paraboloid z = 14 - 5x - 5y and the plane z=9 V= (Type…

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Q: Find the volume of the solid bounded above by the sphere x² + y² + z² 9 and below by the cone z =…

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Q: 4. Use polar coordinates to find the volume of the solid that lies under the paraboloid: z = x² +…

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Q: Let D be a region of a solid between the sphere x2+y2+(z-1)2 = 1 and the hemisphere x2+y2+z2 = 4,…

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Q: Calculate, by means of cylindrical or polar coordinates, the volume of the solid that is inferiorly…

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Q: Find the volume of the solid bounded by the paraboloid z=x2+y2 and the plane 6x+8y-z=21

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Q: Find the volume of the solid below the paraboloid z = x² + y² and above the triangular region R…

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