The area bounded by the curve y = x3,y = 0 & x = 1, is revolved about Oy. Find the volume generated. Sketch the curve indicating the generating area.

Q: Find the volume of revolution obtained by rotating the area between the functions y = = x², x = 2…

A: Given: y=x2n=4y=2n=24=4y=0

Q: Draw the area bounded by the function y = x^2 + 1 and the line y = 2, and then calculate the volume…

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Q: Find the volume formed by rotating the region enclosed by 10y and y = x with y > 0 about the y-axis…

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Q: Find the volume of the solid that results when the area of the region enclosed by y= Vx+1, x = 4,…

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Q: Rotate a circle of radius r around the x axis and use the method of disks to prove the formula for…

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Q: Find the volume of the solid that results when the region enclosed by y = Vx, y = 0, and x = 9 is…

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Q: Find the volume “V” obtained by revolutionizing the region between y=2√x  y  y=x around the x=-2…

A: To find volume obtained by revolutionizing the region between y=2x and y=x around x=-2. y=2xSquaring…

Q: Find the volume generated by rotating the given region about the specified line. R about y = 0

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Q: Find the volume generated by rotating the given region about the spcified line. R about y=0

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Q: Sketch the region bounded by the curves: y = e*,y= lnx,x = 1 and x = then find, the area of this…

A: The graph of the region given can be drawn as

Q: what is the volume generated if the area bounded by the cirves x2 =8y , x=4 and y= 0 is resolved…

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Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

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Q: Find the volume of the solid generated when the region enclosed by y = sqrt(x), y = 0, and x = 49 is…

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Q: Find the volume produced by rotating the bounded region around the line y = 3 in the first quadrant…

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Q: Given the area in the first quadrant bounded by the curve x2 = 8y, the line x = 4 and the x – axis.…

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Q: Find the volume of the solid formed by rotating the region enclosed by eA# + 5, y = 0, x = 0, x =…

A: olume by shell method is given below

Q: Find the volume of the solid generated when the region enclosed by y = -√√x + 1, y = 0, and x = = 2…

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Q: If the region enclosed by the y-axis, the line y=2 and the curve y=sqrtx is revolved about the…

A: Proceed as shown below...

Q: Find the volume of the solid that results when the region enclosed by x = y² and x = y is revolved…

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Q: Find the volume of the solid that results when the region enclosed by x = y² and x y is revolved…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: For the area bounded by y2=4x and y=x, find the volume generated if it is revolved about the line…

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Q: A region bounded byf (y) = Vỹ + 1, y = 4, y = 9, and x = 1 is shown. What is the volume of the solid…

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Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 4x + 8y = 8,…

A: We need to find volume.

Q: Find the volume generated by rotating the area bounded by y = ,* = 2, x = 7, and y = 0 about the y…

A: The solid obtained by rotating the region between the grah of fx and the x-axis from x=a to x=b…

Q: Let A be the area in the first quadrant bounded by the y-axis, the line y=5 x, and the line y=2…

A: Suppose a region is enclosed by two curves, y=fx and y=gx. To calculate the volume of the region…

Q: Find the volume of the solid generated when the region enclosed by y=x^3, x=1, and y=0 is revolved…

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Q: Find the volume (in cubic units) of the region bounded by the curves (y-1)' = x – 1 ,and the lines y…

A: We have to find the volume of the region bounded by curvesy-12=x-1 and lines y=-1 and y=2when…

Q: Find the volume of the solid that results when the region enclosed by x = y? and x = y is revolved…

A: Since there is more than one question asked , I will solve the first one.

Q: Find the volume between the cylinders x+y =1 and the cylinder x* +z* = 1 in the first octant. 2

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Q: Find the volume of the solid formed when the region bounded by the curve y? = x, the line y = 1 and…

A: Definite integrals can be used to compute areas and volumes of solids of revolution. Cylindrical…

Q: Find the volume formed by rotating the region enclosed by * = 11y and y = ¤ with y > 0 about the…

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Q: Find the volume formed by rotating the region enclosed by: 5y and y = x with y > 0 about the y-axis…

A: Given Data The first equation is x=5y. The second equation is y3=x.   Equate the given both…

Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

A: When x=5 then  x=y255=y25y2=25y=5 So y is from 0 to 5 in the figure.

Q: find the volume (in units 3) generated when the region between the curves is rotated around the…

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Q: Find the volume of the solid generated by revolving the region bounded by the curve y = In x, the…

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Q: The area enclosed by y = 4x - x^2 and 2y = 2x + x^2 is revolved about the line x = -1. Using a…

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Q: Find the volume generated by revolving the area bounded by xy=4, x=1, x=4 and the x-axis about the…

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Q: Find the volume of the solid that results when the region enclosed by x = y² and x = y is revolved…

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Q: Given the area in the first quadrant bound by x² = 8y, the line x = 3 and the x-axis. What is the…

A: Use the formula for volume obtained on revolving a dingle function. Determine the limits and the…

Q: Given the area of the first quadrant bounded by x² = 8y, the line x = 4, and the x-axis. What is the…

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Q: Find the volume generated by rotating the given region about the specified line. R about y =0

A: Do integration to find the area between two curve.

Q: Given the area in the first quadrant bounded by x2 8y, the line y - 2 = 0 and the y-axis. What is…

A: The equation of the curves are C1: x2 = 8y ⇒ y = x28C2: y-2 = 0 ⇒ y = 2 Axis of revolution: x-axis…

Q: Find the volume of the solid of revolution below. (1,1) 0.5 y = x³ 1 -0.5 X = X 0.5 1.5 2

A: Given: Apply the disk method to find he volume of the solid about the x-axis.…

Q: Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 25 about the y-axis.

A: Consider the given equation of the circle and find function f(x). Plot the function f(x) and find…

Q: Find the volume, if an area bounded by an asteroid I = cos t y = sin³ t ve y = -/I+x ,y-axis, and…

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Q: Find the volume generated by revolving the area bounded by   xy=4, x=1, x=4 and the x-axis about the…

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Q: Given the area in the first quadrant bounded by x²=8y, the line y-2=0 and the y-axis, what is the…

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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…