Find the volume of the solid that is formed when the following bounded region is revolved about the line x = -1 y = x³ x = 2 y = 0 Show work by graphing the bounded region, indicating the axis of revolution, and drawing the rectangular slices you are adding up.

Q: Find the volume of the solid that results when the region bounded by x = y and x = y + 12 is…

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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: Draw the area bounded by function y = x^2 + 1 and line y = 5, then calculate the volume of the solid…

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Q: Find the volume of the region that results when the region bounded by the curve 4x=y^3 and the line…

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Q: Find the volume of the region that results when the region bounded by the curve x=y^3 and the line…

A: Find the cross sectional area and use it to find the volume.

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…

Q: Find the volume (in cubic units) of the region bounded by the curves (x – 1) = 20 – 4y and the lines…

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Q: Find the volume of the solid generated when the region bounded by x = - sqrt(4y) . y = 4 and x= 0 is…

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Q: Find the volume when the region bounded by y = 2x², x = 0, x = 4, and y = 0 is revolved about the…

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

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Q: ) Find the volume of the solid whose base is the region in the first quadrant bounded by y = x5, y =…

A: Here, the cross-sections perpendicular to the x-axis are semicircles whose base span from y=x5 &…

Q: find the volume of the region enclosed by the curves y=x^3 and y=sqrt x, rotated about the line y=1.

A: We first sketch the region using a graphing calculator  y=x3 (violet) y=sqrt(x) (black) y=1, (red)…

Q: Find the volume of the solid generated when the region bounded by y = 9 – x and y = 2x + 6 is…

A: To find the volume of solid generated by revolving around the x axis

Q: Find the volume of the solid generated when the region bounded by y = 9x and y = 36/x is revolved…

A: The given curves fx=36xgx=9x Solving the above equation 36x=9x362x-81x2=0x362-81x=0x=0, 16

Q: Find the volume formed by rotating the region enclosed by: 6.2y and y° = x with y > 0 about the…

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Q: Find the volume of the solid whose base is the region bounded by the x-axis and the curve y=e^x…

A: It is given that:

Q: Find the volume of the solid generated when the region between the lines: x = 3, x = 5, y = 2,y = 4…

A: Given: The line equations are x=3, x=5, y=2 and y = 4   To find: The volume of the solid generated…

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: Determine the volume of the solid generated when the region bounded by the curve y? = x³ and the…

A: Given that, y2 = x3, the x-axis revolved about the x-axis.

Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y 1, and the…

A: Here, to find the volume of the solid whose base is the region in the first quadrant bounded by…

Q: Use the best method available to find the volume. The region bounded by y = 10- x, y 10 and y x…

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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 generated when the region bounded by y=4x and y=16sqrt(x) is revolved…

A: The given curves are: y=4x    and    y=16x The intersection point of both curves are: (0,0)  and…

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: Find the volume of the solid generated when the region bounded by y = 5x and y= 15√√x is revolved…

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

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Q: Find the volume of the region bounded by y=x^3 and y=x rotated about the x-axis.

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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 of the solid whose base is the region bounded between the curves y = x and y = x²,…

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Q: Find the volume of the region bounded by y = Vx and y = x rotated about the x-axis.

A: The graph is where red curve represents y=x and blue line represents y=x.

Q: Find the volume of the solid generated byrevolving the region in the first quadrant bounded by the…

A: Using Shell Method:             2π∫01x.e-x dx Limits come from where the column can be created. (in…

Q: Find the volume when the region bounded by the y=√(3x) and y=√(3−x) is rotated about the x axis.

A: To calculate the volume of the region bounded by the given curves when rotated around x-axis.

Q: Let M be the region in the first quadrant bounded by the graphs of y=arctanx and y=(πx)/4. What is…

A: Given, y=tan-1xy=πx4 Revolving around x=2   To find: The volume of rotation of the bounded region.…

Q: Find the volume of the solid that results when the region enclosed by y = Vx, y = 0, and x = 81 is…

A: We have to find the volume of region.

Q: Find the volume obtained by rotating the region bounded by the curves x = y² and y = x³ about the…

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Q: Find the volume of the region bounded by: x y +1 that is rotated about the x-axis.

A: Use volume formula about x axis

Q: The region bounded by the curve (y = x2 + 5) and the line (y = x+7) is revolved about x-axis to…

A: The intersection points of the given curve and the line is calculated as follows:…

Q: Find the volume of the solid that results when the region bounded by v-x1=0 and x=l04 is revolved…

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Q: Find the volume of the solid generated when the region enclosed by y = sqrt(x+1), y = sqrt(5x), and…

A: The volume of the region bounded by the curves y1(x) and y2(x) is given by the formula…

Q: Find the volume of the solid generated when the region enclosed by y = sqrt(2x + 8), y = x, x = 0 is…

A: Given :     To find the volume of the solid.

Q: (b) Determine the volume of the solid that results when the region enclosed [2] by the curves y = x²…

A: Solution:Given   y=x2+2   and y=4-x2and th line y=3To determine the volume of the…

Q: find the volume of the solid that results when the region enclosed by the curves x=y2 and x=y+2 are…

A: Given curves are x=y2 and x=y+2          (1) f(y)=y2 and g(y)=y+2 From (1)…

Q: Find the volume of the solid obtained when the region bounded by the line y = 2x, the line x = 3,…

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Q: Let y = √r and y = 2³, draw the region bounded by the curves. Then, use the washer method to find…

A: In this question we have to find the volume of the region bounded by curves using washer method. The…

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: The volume of the solid generated when the region at the first quadrant bounded by the curve y = x²…

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Q: Use the best method available to find the volume. The region bounded by y 8-x, y 8 and y =x revolved…

A: We have to find the volume of the region bounded by y=8-x, y=8 and y=x evolved about y-axis. Draw…

Q: Find the volume of the solid that results when the region bounded by y = x and y = x², from x = 0 to…

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Q: Consider the 2D region bounded by y = x5/2, y = 0 and x = 4. Use disks or washers to find the volume…

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