11. y = x, x =0, y = 5; about x-axis

Q: Use the shell Method to find the volume of the solid generated by revolving the area bounded by the…

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Q: Find the volume of the solid generated when the plane region bounded by x = y? and x + y = 2 is…

A: To find the volume of the solid generated when the plane region bounded by  x=y2 and x+y=2 is…

Q: Let R be the region bounded by y = 9 – x and y = 2x+ 6 find the volume %D generated when R revolved…

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Q: Locate the mass center of the homogeneous solid body whose volume is determined by revolving the…

A: here region is rotated about z axis to create the solid  z=Moment about r -axis volume of solid

Q: Find the volume of the region bounded below by the cone ( =V(x² + y²) ‚and above the plane ( z=1),…

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Q: Determine the volume of the solid obtained by rotating the region bounded by y = a? – 4x + 5, a = 1,…

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Q: Find the volume of the solid generated by revolving the given plane area having the given boundaries…

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Q: y? = 4x, y = 2x - 4; about y-axis

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Find the volume of the solid formed by rotating the region enclosed by y = e* + 3, y = 0, z = 0, z =…

A: This volume of solid of revolution can be obtained by the method of cylindrical shells as explained…

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: By Sketching the graph, find the volume of the solid generated by revolving the region given by, y =…

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Q: Find the volume and centroid generated by revolving the given plane area about the indicated axis: x…

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Q: Find the volume of the solid bounded by the paraboloid z = 16 – 2? – y, the cylinder 2 + y? 8 and…

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Q: The volume under the plane z – a? – 2y? = 0 and above the region enclosed by the line y = x – 458…

A: To find the volume under the plane z-x2-2y2=0 i.e. z=x2+2y2 and above the region enclosed by the…

Q: Find the volume of the solid generated when the region enclosed by y = Vx + 1, y = V5x, and y 0 is…

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Q: Find the volumes of the solids generated by revolving the shaded regions about the indicated axes.

A: Find the volume of resulting solid. x=tanyV=∫abπRy2-ry2dyRy=1 outer radiusry=tany inner…

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by z = 0,…

A: Given :   The regions in the first quadrant bounded by   x = 0  , y = 1  , x = y5   To determine :…

Q: Find the volume of the solid bounded below by the circular paraboloid z = x? + y? and abov the…

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Q: find the volume of the solid generated when R is revolved about the x-axis

A: Given that R is the region enclosed by the curve y=cosx, y=ex, x=π2 The volume of the solid…

Q: Find the volume bounded below by the paraboloid z= x? + y? & above by the plane z=2y ?

A: The objective is to compute the volume below by the paraboloid z=x2+y2 and above by the plane z=2y.

Q: Find the volume of the region bounded below by the cone ( z=V(x2 + y?) ,and above the plane ( z=1),…

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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 formed by rotating the region inside the first quadrant enclosed b y=x,…

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Q: 5. x=9-y', x-y-7= 0 about x = 4

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Q: 4. y= 6x- x', y = x? - 2x, y = -1

A: We find the volume.

Q: 4. y= 6x -x², y = x² – 2x , y = -1

A: Given that     y = 6x-x2 , y=x2-2x , y=-1 Here we have to find the volume and the centroid.

Q: Find the volumes of the solids generated by revolving the region between y = 2√x and y=- about a)…

A: Solution

Q: УА СО), 1) В(1, 1) y vx R3 yr о х A1, 0 Referring to the figure above, find the volume generated by…

A: To calculate the volume generated by rotating the region R2 from given figure about BC.

Q: use the disk method to find the volume (in units^3) when the regionbounded by the curves x+y=5, x=0,…

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Q: Locate the mass center of the homogeneous solid body whose volume is determined by revolving the…

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

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Q: ). y = x² +1, x=0, y = 5; about y-axis

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Q: Find the volume of the solid bounded by the paraboloid z = 24 – x? – y², the cylinder x? + y? = 12…

A: Ans is 216 pi

Q: Find the volume of the solid that lies within the sphere x2 + y2 + z² = 36, above the xy-plane, and…

A: The sphere is x2+y2+z2=36 and cone is z=x23+y23. Substitute x=ρsinϕcosθ,y=ρsinϕsinθ,z=ρcosϕ in…

Q: 13. y? = 5-x, x=0; about x = 5

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Q: The integral represents the volume of a solid of revolution. 14 27T (a) Identify the plane region…

A: We are asked to find the region that revolved.

Q: Find the volume of the region bounded below by the cone ( z=V(x² + y²) ‚and above the plane ( z=1),…

A: Volume of cone = (πr2h)/3

Q: Find the volume bounded below by the paraboloid z= x? + y & above by the plane z=2y ?

A: The volume for the given question has been obtained in step 2.

Q: 7. y' = 4x, x = 4; about x = 4

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Q: Use the disk or the shell method to find the volume of the solid generated by revolving the region…

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Q: Find the volume of the solid bounded from above by the paraboloid z = 6 – a2 – y?, inside the…

A: In general volume, integrals are triple integral, which involves the integral with respect to x,y,…

Q: Use the disk or the shell method to find the volume of the solid generated by revolving the region…

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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 generated by revolving the shaded region about the given axis.

A: We need to find volume.

Q: Find the volume of the cap of a sphere with radius R and height h using a triple integral. R.

A: Consider the following figure By Pythagorean theorem x2+y2=R2 ⇒x2=R2−y2

Q: Find the volume of the solid generated bounded by x = Jy – 1, x = y? – 2y + 1, rotated about the x-…

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Q: Locate the mass center of the homogeneous solid body whose volume is determined by revolving the…

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Q: Find the volume of the solid that is created by rotating the area enclosed by y = Vx + 3, y = 3, and…

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Q: 9. Find the volume generated by revolving the given plane area about the given line using the disc…

A: We are given two regions: (a) y=2x2, y=0, x=0, x=5 about x-axis. (b) x2-y2=16, y=0, x=8 about…