Find the volume of the solid S under z = 3 + 2 cos x^2 and restricted by a triangle in the xy-plane with the vertices (0, 0),(6, 0) and (6, 2).

Q: Find the volume of the solid bounded by the graphs of r = 3 sin 30, : = 4 + Vx2 + v², = = 0, in the…

A: First, plot the graphs of the given functions. Then, identify the limits.

Q: Find the volume of the solid bounded above by f(x,y) = 5x², below by the xy-plane and the sides by y…

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Q: Find the volume of the solid generated by the region bounded by y - x² = -3,x+y = 3 about y = -5.

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Q: . A solid is formed in the first octant bounded by the plane z = 6 – x – y and the cylinder y = 4 –…

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Q: ) Determine the volume of the solid bounded by x = -4, z = 4, x = -y², and the xy-plane.

A: Given: a solid bounded by x=-4, z=4, x=-y2 and the xy plane. To find : volume of the solid   In the…

Q: Find the volume of the solid bounded by the plane 2x + 8y + 5z = 2 in the first octant. Leave your…

A: Equation of plane, 2x + 8y + 5z =2

Q: Find the volume of solid lying in the first octant bounded by the graphs of : z = 4 – x2 – y² , y =…

A: The volume of the solid in first quadrant is given by: V=∫ab∫cdf(z)dydx Now, find the range of the…

Q: Use a triple integral to find the volume of the solid bounded by the graphs of the equations. z = 9…

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Q: Find the volume of the solid in the first octant bounded by the coordinate planes, the plane x = 3,…

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Q: Find the volume of the solid bounded by the plane 3x + 8y + 4z = 10 in the first octant. Leave your…

A: In the given problem the first octant denotes the region in the coordinated plane where x,y,z≥0 The…

Q: Find the volume of the region under the surface z = 6x° and above the triangle in the xy-plane with…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: According to our guidelines we can answer only first three subparts.

Q: Find the volume of the solid bounded by the elliptic cylinder 4x2 + z2 = 4 and the planes y = 0 and…

A: According to the given information, it is required to find the volume of the solid bounded by…

Q: Use a double integral to calculate the volume of the solid in the first octant bounded by the…

A: We have to find volume of solid in first octant with the help of double integral-

Q: Find the volume of the region under the surface z and above the triangle in the xy-plane with 1+ x²…

A: We have to find the volume of the region under the surface.

Q: Find the volume of the solid above the triangle with vertices (0, 0), (1, 0) and (1, 2), below the…

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Q: Find the volume of the solid that is bounded above by the cylinderz = x2 and below by the region…

A: Given, bounded region z=x2, y=2-x2, y=x region can be define as ∫∫x2dxdy now region is y=2-x2, y=x…

Q: Find the volume of the region under the surface z = 4x* and above the triangle in the xy-plane with…

A: The solution follows as

Q: Find the volume of the solid generated by revolving the area bounded by x- y² + 4y-4 0 and x- y-4 0…

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Q: Find the centroid of the volume generated by revolving about the line x = 1, the area bounded by x2-…

A: We will use basic integral calculus and techniques of integration to answer this question.

Q: A solid is formed in the first octant bounded by the plane z = 6 - r - y and the cylinder y = 4 –…

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Q: Find the volume of the solid in the first octant bounded by the coordinate planes and the passing…

A: Given- 1,0,00,2,0 and 0,0,3 To find- The volume of the solid in the first octant bounded by the…

Q: . Find the volume of the solid bounded on the front and back by the planes x = above by the cylinder…

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Q: Find the volume of the solid bounded above by f(x,y) = 3x2, below by the xy-plane and the sides by y…

A: Let's find.

Q: Find the volume of the solid in the first octant bounded by 2x + 3y + 4z = 12 and the coordinate…

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Q: Find the volume of the solid bounded from up by surface f (x,y) = 2x + y2 and from below by the…

A: According to question, surface :f(x, y) = 2x+ y2,Traingle vertices : 0, 2, 0, 0 and 3, 2

Q: Find the volume of the solid bounded by the plane 4x + 6y + 7z = 9 in the first octant. Leave your…

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Q: A solid is formed in the first octant bounded by the plane z = 6 - x - y and the cylinder 4 - x².…

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Q: Find the volume of solid lying in the first octant bounded by the graphs of : z = 4-x2-y2, y= 2-2x2,…

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Q: Express the volume of region bounded by the solid 2x + y + 4z2 = 4, the plane y = 2 and the yz-plane…

A: The volume between surfaces can be calculated using the triple integral. The triple integral in…

Q: Find the volume of the solid in the first octant bounded by the parabolic cylinder z = 25 - x^2 and…

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Q: Find the volume of the solid bounded by the plane 9x + 3y + 3z = 6 in the first octant. Leave your…

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Q: Find volume of the solid bounded by z = 0, f(x,y) = x2 +y2, x2 + y2 = 52, 3y = -2x and 20y = 8x…

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Q: Find the volume of the solid generated by revolving the area bounded by x2 – 2kx – 4ky + k2 = 0 and…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Use a triple integral to find the volume of the solid bounded by the graphs of the equations. z = 5…

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Q: Find the volume of the solid bounded above by f(x,y) = 7x2, below by the xy-plane and the sides by y…

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Q: 6) Use double integral to find the volume of the solid bounded above by the paraboloid 9x² + y²,…

A: We can find the volume of the solid by using double integral .

Q: Find the volume of the region under the surface z = and above the triangle in the xy-plane with 1+x2…

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Q: A solid is formed in the first octant bounded by the plane z = 6 – r - y and the cylinder y = 4 –…

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Q: Find the centroid of the volume generated by revolving about the x=1, the area bounded by…

A: Answer is mentioned below

Q: Find the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2 and the plane x…

A: Given Data The equation of the cylinder is z=12-3y². The equation of the plane is x+y=2.   Let, The…

Q: Find the volume of the given solid. Bounded by the cylinders z = 3x2, y = x2 and the planes z = 0, y…

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Q: Find the volume of the solid bounded by the plane 8x + 5y + 10z = 7 in the first octant. Leave your…

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Q: Compute the volume of the solid bounded above by z = 8xy° and below by the triangle with vertices

A: In this question we will use basic of calculus i.e application of integration. We will plot the…

Q: Find the volume of the solid bounded by the plane 7x + 3y + 4z = 3 in the first octant. Leave your…

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Q: Find volume of the solid bounded by z = 0, f(x,y) = x² +y², x² + y² = 4?, 4y = -5x and 13y = 6x…

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Q: Find the volume of the solid in the first octant bounded by the parabolic cylinder z= 25 - x and the…

A: Since we are considering only in the first octant so lower limit of both x and y will be zero.…