The region bounded by the parabola y = x and the line y = 2x is revolved about the line y = -1. Find its volume generated.

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

Q: The region bounded by the graphs of y=x^2 and y=6-|x| is revolves around the y-axis. What is the…

A: solution is given below

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

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Q: Find the volume of the solid obtained when the region bounded by the curves y = x^4 − 2x and y = 0…

A: We have to find the volume of of the solid of revolution of the region bounded by the curves y=x4-2x…

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Q: The area bounded by the parabola x^2-2x+y=3, in the second quadrant about the line y=4. Find the…

A: Consider the given curve: y=-x2+2x+3 Here, the objective is to find the volume of solid formed by…

Q: The area bounded by y = 2x² - x³, and y=0 is revolved about x=0. Find the volume of the solid…

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Q: The region in the first quadrant that is bounded above by the curve y = 1/(x^1/2), on the left by the…

A: Given that the function  y = 1x, x = 14 , y =1

Q: . THe area enclased by the loop of the curved y= x (x - 3)° is Find the volume generated . revolved…

A: Here 1st we will find points where loop is formed and then shade the region bounded ,  To form the…

Q: Find the volume generated by revolving the region above the curve y=x3 , under the line y=1, and…

A: Given: y=x3, y=1, x=0 & x=1 From the given curve the bounded region is as shown below: Apply…

Q: Find the volume of the solid generated when the region bounded by y = x² – x and y = x - y2 is…

A: Introduction: If the area of the ring is A=πOuter radius2-(Inner radius)2, the volume of solid…

Q: Find the volume formed by revolving about the line y = 2a, the area %3D bounded by that line, 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…

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

Q: What is the volume (in πcu. units) of the region bounded by the curve y=x^3, and the lines x=1, x=2…

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Q: y = 9x² and y = 0 about x = −4

A: Given:        y=9-x2 and y=0         x2=9           x=3 about x=-4

Q: Find the volume generated if the area bounded by the curve y=x^2 and the line y=2x+3 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…

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Q: Find the volume of the solid generated from revovling the area of the region bounded by the curve y…

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Q: Find the volume generated if the area of the region bounded by y= 1/x, y=x/4 and x=3 is revolved…

A: To calculate the volume of the surface of revolution, first obtain the bounds of the surface that is…

Q: Find the volume of the solid generated by revolving the region between the parabola x=y^2+1 and the…

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Q: What is the volume of the solid generated when the region bounded by the graph of x = √y - 2 and the…

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Q: Find the volume of the solid obtained when the region bounded by the x-axis, the y-axis, and the…

A: We have to find volume of the solid bounded by given region

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

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

Q: y = x4; and y = 1 about y = 2

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Q: The region in the first quadrant that is bounded above by the curve y = 1/(x^1/4) , on the left by…

A: Solution Given The region in the first quadrant that is bounded above by the curve y = 1/(x^1/4) , on…

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A: Volume is the measure of the amount of space occupied by a closed surface. It is measured in terms…

Q: Find the volume of the solids of revolution generated when the region bounded by the curve y = x^2 ,…

A: Here we have to find the volume of the solids of revolution generated when the region bounded by the…

Q: The area bounded by the curve y^2 = 12x and the line x = 3 is revolved about the line x =3. What is…

A: Recall: Formula for volume,    V=π∫ab(radius)2dy Given,  y2=12x Substitute x=3 in the above…

Q: Find the volume generated by rotating the region between the graphs of y = 2 - x, x = 0, and the…

A: Consider the provided region, y=2-x,x=0 Find the volume generated by rotating the region between the…

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y=x^2 and…

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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: The region bounded by the curve y = x and the line y = 3x, is revolved about the line x=-3. Find its…

A: Given functions are                                                         y=x2y=3xx=-3 points of…

Q: Find the volume generated by the region bounded by the curve y 12X and the line X3 rotated about the…

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Q: Find the volume generated by the area bounded by the y-axis, the line y=1, and the arc of y=sin x…

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Q: The area bounded by y = x3 + 2x + 1, x = 1 and x = 3 is to be revolved about the x-axis. Find the…

A: Given problem:- The area bounded by y = x3 + 2x + 1, x = 1 and x = 3 is to be revolved about the…

Q: 4. Find the volume of the solid whose base is the region enclosed between the curve x = 1-y² and the…

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

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Q: Find the volume of the solid obtained when the region bounded by the curves y =−x^2 + 2x + 3, y = 0…

A: Given: The curve is: y=-x2+2x+3 and y=0 Now, the point on x, when y=0 are:…

Q: Find the volume (in cubic units) of the region bounded by the curves y' = 4x and the line X = y when…

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Q: Find the volume generated when the area bounded by the curve y2=x , the line x=4 and the x-axis is…

A: Volume bounded by the curves, about y-axis.using Disk method

Q: Determine the volume produced by the region bordered by x² - 4x - 4y + 4 = 0 and y = 1 about the…

A: We will use disk method to find volume of solid generated

Q: Find the volume of the solid generated by revolving the region bounded by the parabola y = 2x2 and…

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Q: Find the volume of the solid obtained when the region enclosed by the curve x=2-y² and find the x=y…

A: Draw the sketch of the given curve and lines.

Q: Find the volume of solid formed when the region bounded by y = x² and y = Vx are revolved about…

A: To find the volume of solid formed when the region bounded by y=x2 and are revolved about x-axis…

Q: Find the volume of the solid generated when the region bounded by y=x²-x and y=x-x² is revolved…

A: bounds are  x = 2 ,   y=x²-x   and   y=x-x² y = -(x - x2) y = -y y = 0 =>  x =>   0 = x - x2…

Q: Find the volume formed by revolving the region about the line x = 4. 1 2 3 y = 3 – x & y = -x² + 2x…

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