Find the volume V under the the plane z = 8x + 6y over the region R = (x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 2x^2 using vertical slice (Case 1), and horizontal slice (Case2). Do they give different results?

Q: The volume generated when the region bounded by y = x, y = 1, x = 0 is rotated about x axis is -

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Q: Find the volume of the solid region bounded in the first octant by the plane. z = 12 - x - 4y cubic…

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Q: /consider the region n in the first quadrant Cxzo, y 20) in the xy-plane bounded by x= 2yxニy2ュ1…

A: solution:-the region bounded byx=2y2,  x=y2+1 androtating about the line y=-3using cylindrical shell…

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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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 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 solid bounded by y=2x+1,y=3and x=4 about  line y=10usingthe cylindrical shell…

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Q: Find the volume of the solid generated by revolving the triangularregion bounded by the lines y =…

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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: Find the volume of the solid bounded above by the z=2−x plane and below by the x=4−y^2 curve, in the…

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Q: Find the volume above the xy-plane bounded by the surfaces: 3 2a ²+y² = a², z =y and z= 0. Ans.

A: Given,

Q: Find the volume of solid generated by revolving the region bounded by y=x+3, y=4 and x=5 about the…

A: We first sketch the region using a graphing calculator   The shaded region is rotating about the…

Q: Find the volume of the solid generated when the area bounded by the given curves and lines is…

A: x=9-y2,y=1, y=3, x=0 about y axis

Q: Find the volume of the solid bounded above by f(x,y) = 8x², below by the xy-plane and the sides by y…

A: Volume

Q: Find the volume of the region bounded by z = 4 - x² - y and the xy plane.

A: Given the region bounded by z=4-x2-y2 and the XY plane

Q: Find the volume of the solid enclosed by the cylinder x+ y = 9, bounded above by the sphere x +y° +=…

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Q: Consider the solid bounded by the plane z = 6 – x – y and the cylinder y = 4 – x². SET UP the double…

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Q: Find the volume of the solid bounded by the plane z = 10 - 5x - 8y and the coordinate planes in the…

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

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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: Find the volume of the solid generated when the area bounded by the given curves and lines is…

A: You have posted multiple questions. As per the instruction, we will be answering only the first…

Q: Find the volume of the solid bounded above by the plane z = (1+x2+y2)2 and below by the plain z =0…

A: Let V be the volume of the solid which is bounded above by  z=21+x2+y22 and below by z=0 over the…

Q: Compute the volume of the solid generated by revolving the triangularregion bounded by the lines 2y…

A: Compute the volume of the solid generated by revolving the triangularregion bounded by the lines 2y…

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 of revolution bounded by the cirde x+y = 16, and the lines z = 0 and 8,…

A: Given curve is x2+y2=16 and line x=0 and x=8 about x-axis We have to find the volume of the solid of…

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: Calculate the volume of the region bounded by the spherex + y² + z² = 9 from above and by the cone…

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Q: Suppose the disk method is used to find the volume of the solid obtained when the region bounded by…

A: Given the curve x=y2 and the line x = 4

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 solid bounded above by f(x,y) = 4x?, below by the xy-plane and the sides by y…

A: We will find out the required volume.

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: Plot the curves to find the area of the bounded region formed by the curves.

Q: Find the volume of the solid in the first octant bounded above by the plane x + z = 8 and laterally…

A: Find the volume of the solid in the first octant bounded above by the plane x + z = 8 and laterally…

Q: Find the volume of the solid bounded by y=x2+1y=x2+1 and the line y=−x+3y=−x+3, revolved about the…

A: Given curves are y=x2+1 and y=-x+3 and the line y=5 Find the volume

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: Find the volume of the solid bounded above by the cylinder y = x2 and below by the region enclosed…

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Q: Use cylindrical coordinates to compute the volume of the region defined by 4 - x² – y² <zs 10 – 4x2…

A: We have to compute the volume of the region defined by 4−x2−y2≤z≤10−4x2−4y2. Let x=rcosθ and y=rsinθ…

Q: Find the volume of the region under the surface z = 9x and above the triangle in the xy-plane with…

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Q: What is the volume of the region coming from the cylinder {(x, y, z) : x^2 +y^2 ≤ 1} sliced by the…

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Q: Find the volume of the solid bounded above by the plane z = and below by the plain z = 0 over the…

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

A: The required region is as shown below:

Q: Find the volume of the solid obtained by rotating the region bounded by given sets of curves. y = 2x…

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Q: 2 Sketch the volume bounded by the surfaces +z = 1, y = 2z = 2 in the fir and set up the bounds for…

A: Let D be a closed, bounded region in space. Let a and b be real numbers, let g1(x) and g2(x) be…

Q: Find the volume of the solid bounded by the plane 7x + 3y + 8z = 3 in the first octant. Leave your…

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Q: Find the volume of the solid generated when the area bounded by the given curves and lines is…

A: x=9-y2, y=1, y=3, x=0 about the y-axis

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 the volume of the solid capped by the surface z = 1 – y – x² over the region bounded on the xy-…

A: To find the volume of the solid capped by the surface z = 1 - y - x2 over the region bounded on…

Q: Find the volume of the solid region bounded in the first octant by the plane. z = 12 - x - 3y X…

A: The question is from the topic advanced calculus