Find the volume of the solid that lies under the paraboloid z = x + 3y and above the region x = y and y = x

Q: Find the volume of the solid that lies under the paraboloid z = x² + 3y² and above the region D =…

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Q: find the volume of the given solid under the plane 3x+2y-z=0 and above the region bounded by y=x and…

A: Consider the given plane equation 3x+2y-z=0. Express the given plane equation as follows.…

Q: Find the volume of the region bounded above by the sphere x2 + y2 + z2 = 2 and below by the…

A: At the outset, let me tell you that the question has a typo error or you have not pasted the…

Q: Find the volume of the solid obtained by rotating the region about the x-axis bounded by the graphs…

A: The volume of solid of revolution rotated about x-axis can be given by the formula V=∫abπ…

Q: Find the volume of the solid obtained by rotating the region xy = 1, y = 0, x = 1, x = 2 about the…

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Q: Find the volume of the given solid. Under the plane 7x + 2y – z = 0 and above the region enclosed by…

A: To  find the volume of the solid under the plane and between the region

Q: Find the volume of the solid obtained by rotating the region bounded by y = x² , y = 0, and r = 3,…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = VT, y = 1, r = 2, and r…

A: Find the volume rotating about x-axis

Q: Find the volume of the given solid. Under the plane 7x + 2y − z = 0 and above the region enclosed…

A: Given the plane 7x+2y-z=0 and the regio enclosed by the parabolas y=x2 and x=y2

Q: Find the volume of the region bounded by the paraboloid z = x² + y² and the plane x + y = 1 in the…

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Q: Find the volume of the given solid. Under the plane 9x + 2y – z = 0 and above the region enclosed by…

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Q: Discover the volume of the solid region in the first octant bounded by the coordinate planes and the…

A: Equation of given surface = z= 5-x^2-y  dV = dx dy dz

Q: Find the volume under the plane x+ y-z=0 and above the region enclosed by the parabolas y =x² and x=…

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Q: Let R be the region bounded by x=y², x = 0 and y = 2 , then the volume of the solid formed by…

A: I have append the formula used in the solution part.

Q: Find the volume of the region enclosed by the paraboloid (x-1)²+y=z and the plane 2x+z=2.

A: To find the volume of the region enclosed by below paraboloid and the plane. x−12+y2=z and…

Q: Find the volume of the solid whose base in the xy plane is the region bounded by the graphs of y=x²,…

A: Introduction: Volume and the triple integral are equivalent. Integral is mostly used to calculate…

Q: Find the volume of the solid obtained by rotating the region bounded by y = x3, y = 0, and x = 2…

A: Follow the steps.

Q: Find the volume of the solid obtained by rotating the region bounded by I = 4y², y = 1, z = 0, about…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = -1+ In r, y = 2, y = 4,…

A: Given function is : y=-1+lnx , y=2, y=4 To find the volume of solid obtained by rotating the region…

Q: Find the volume V of the solid below the paraboloid z = 4-x² - y² and above the following region. R=…

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Q: Find the volume of the solid under the plane 9x + 3y – z = 0 and above the region bounded by y = x…

A: Solution: y = x y = x4

Q: Find the volume of the solid formed by revolving the region bounded by the graphs y=x and y=x³ from…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = Inr, y=1, y= 4 and r = 0…

A: shaded portion is the region of interest that is rotated around y-axis to make a solid. y=ln(x)…

Q: Find the volume of the solid that lies under the paraboloid z=x5+y5 and above the region y=x2 and…

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Q: Calculate the volume of the solid formed by rotating the region bounded by xy = 2 , xy = 4 , x = 1 ,…

A: Given regions are xy=2, xy=4, x=1 and x=2.

Q: Find the volume of the region bounded below by the plane z = 0, laterally by the cylinder x2 + y2 =…

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Q: Find the volume of the given solid 1. Under the paraboloid z = 3x2 + y? and above the region bounded…

A: Get points of intersection of y=x and x=y2-y: y=y2-yy2-2y=0y=0,2

Q: find the volume of the solid obtained by rotating the region bounded by xy=1, y=0, x=1, x= 2 about…

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Q: Find the volume of the region bounded above by the paraboloid z = 3 - x- y and below by the…

A: Since you have posted multiple questions according to company rule we are supposed to give solution…

Q: Find the volume of the solid under the paraboloid z = 3x? + y² and above the region bounded by the…

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Q: Find the volume of the solid under the plane 9x + 3y – z = 0 and above the region bounded by y = x…

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Q: Find the volume of the solid formed by rotating the region y = Vx, y = 0, x = 1

A: According to question giveny=xy=0x=1As we know that the volume for solid of revolution between…

Q: Find the volume of the solid obtained by rotating the region bounded by y=x+ 1 y=0, and x = 2 about…

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Q: Find the volume of the region bounded above by the elliptical paraboloid z = 6 - 2x² - 2y² and below…

A: We will use limits of x,y,z to create a triple integral to represent volume and then solve it

Q: Calculate the volume of a solid that is under the paraboloid z = x2 + y2, above the xy plane and…

A: Given To calculate the volume of the solid that is under the paraboloid  z = x2 + y2, above the xy…

Q: Use the Shell Method to find the volume of the solid generated when the region bounded by y = 4- y…

A: Find the volume of solid using shell method:

Q: Find 2x dA over the region R = {(r, y) | 0<z< 4,0 < y < 6} by identifying it as the volume of a…

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Q: Find the volume of the solid obtained by rotating the region bounded by the curves = Vx, y = -x +2…

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Q: Find the volume of the solid bounded by the paraboloid z = 16 – x² – y², the cylinder æ? + y² = 8…

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Q: Find the volume of the region that lies above the cone z = √x² + y² and between the spheres x² + y²…

A: Volume is the amount of space occupied by the closed surface. In this problem, the region is bounded…

Q: Find the volume of the solid bounded by y = x² , x = y° , z = x + y + 15, and z = 0.

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Q: Find the volume of the solid that lies under the paraboloid z = x² +y² and above the region D in the…

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Q: y =, x = 1, x = 4, and y = 0 is revolved about the y - axis.

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Q: Find the volume of the solid that lies under the paraboloid z = x² + y? and above the region D in…

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Q: Find the volume of the region bounded above by the paraboloid z = x2 + y2 and below by the triangle…

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Q: Find the volume of the solid obtained by rotating the region bounded by y=x+1 y=0, and x=2 24π C.U.…

A: Answer is 9π c. u.

Q: Find the volume of the solid generated when the plane region bounded by: y=4/x, x=1, x=4, and y=0…

A: Given regions are y=4/x, x=1, x=4 and y=0.

Q: Find the volume of the portion of the solid cylinder x2 + y2&lt;= 1 that lies between the planes z =…

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Q: Find 3dA over the region R {(x, y) | 0 < x < 5,0 < y < 6} by indentifying it as the volume of a…

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Q: Find the volume of the solid under z=4x and above the region bounded by y=x2 , y=4, and x=0

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