1. Find the volume of the solid generated when the region bounded by y = 9-x2 and y = 2x + 6 is revolved about the x-axis.

Q: Let M be the region in the first quadrant bounded by the graph of y=3x+2, the graph of y=x+2, and…

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Q: 5. Find the volume of the solid obtained by rotating about the x - axis of the region bounded by y =…

A: We have to compute the volume of the solid generated by revolving the region bounded by the curve…

Q: 2. Find the volume of the solid generated by revolving the region under the curve f (x) = x² + 1…

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Q: Let A1 be the region bounded by y = 5x (1−x) 2 and the x-axis between x= 0 and x= 1. Find the…

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Q: 7. Find the volume of the solid obtained by rotating the region under the graph of f (x) = 9 – x2…

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Q: 1. Find the exact volume of the solid formed by revolving the region bounded by the graphs of y = x'…

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Q: Consider the region bounded by the graphs of y=In x, x-1, and y=1. Which of the following integrals…

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Q: 2. Find the volume of the solid obtained when the region between the graph the y = f (x) = Vĩ and y…

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Q: (#3) Find the volume of the solid generated by f(x) =x° and f(x) = 4x-x° rotating about the y-axis:

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Q: 3 14. Find the volume of the solid that results when the region bound by y = x°, x = 2 and the…

A: The given region is the region bounded by y=x3,x-axis y=0 and x=2. To find the volume when the…

Q: 4. (a) Find the volume of the solid generated when the region enclosed by y = -. 6-x2 and y = 0 is…

A: Given the solid generated when the region enclosed by  y=−6−x225  and  y=0   is revolved around the…

Q: Find the volume of the resulting solid if the region under the curve 6 y = 2 x + 3x + 2 from x = 0…

A: To the  find volume.

Q: 1/ Draw the functions , 2/ Find the volume of the solid generated by revolving region bounded by…

A: the given question is taken from calculus in which we have to find the volume of solid generated by…

Q: - Find the volume of the solid generated by revolving about the line x = 1 the region bounded by the…

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Q: The region bounded by the curves x^2+4y=8 and (x-4)^2=4y+8 is revolved about the line y=3. Determine…

A: The region bounded by curves:

Q: 12. Find the volume of the solid that results when the region bound by x 1-y and the y-axis is…

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Q: 1- Find the volume of the solid obtained by rotating the region bounded by the curve y = cos x and…

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Q: 5. Use the method of Washers and Shells to find the volume of the solid generated when the region R…

A: Given:

Q: Consider the region bounded by the graphs of y = ln x, y = 0, and x = e. c. Find the volume of the…

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Q: 4- Find the volume of the solid obtained by rotating about the x-axis the region under the curve y =…

A: Given curve, y=5x from 0 to 4.

Q: 1. Find the volume of the solid generated when the region bounded by y = ex, x = 0, x = 2 and the…

A: Note: As per our guidelines we are instructed to solve only one problem. Hope you understand.    The…

Q: 4. Find the volume of the solid generated when the region bounded X - 2 by f(x) = x = 1, and the…

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Q: 9. Find the volume of the solid obtained by rotating the region bounded by y = Vx. x 0, and x = 4…

A: To find: The volume of the solid obtain by rotating the region bounded by y=x, x=0 and x=4 about the…

Q: 2.4. Find the volume of the solid generated by revolving the region bounded by y = 5a about the…

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Q: Find the volume using the disk or washer method

A: Find the volume of the solid obtained by rotating region.

Q: 12) Find the volume of the solid bounded by x² +y² = 4 and z=x+y in the first octant.

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Q: 2. Find the volume of the solid in the first octant bounded by the cylinder z = sin(y) when 0 < y <n…

A: To find the volume of the solid

Q: 1. Find the volume of the solid generated when the region bounded by y = 9 - x? and y = 2x + 6 is…

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Q: 2. Find the volume of the solid generated when the region between y = sin x and y = 0 for 0 ≤ x ≤ π…

A: The region between y=sin x and y=0 for 0≤x≤π is revolved about the y-axis.

Q: 4. Find the volume of the solid formed by rotating the region under the graph of f(x) = 1 on [0, 3]…

A: Volume of a solid generated by rotating the graph of a function can be determined using the method…

Q: 4) Find the volume of a solid generated by revolving about the x- axis the region bounded by y = x2…

A: We find the volume of a solid generated by revolving about the x- axis the region bounded by y = x2…

Q: - The region bounded by 2y = x and (x − 2)² = −4y + 12 is revolved about the line y = 4. Determine…

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Q: Given a curve having an equation of y2 = 4x. a) Compute the area bounded by the curve and the line…

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Q: Find the volume of the solid generated when the region bounded by x2=8y and x=2y-8 is revolved about…

A: The graph for this is as follows :

Q: 1 Find the volume generated when the area bounded by y=√√x and y=-x is rotated around the x-axis 2 A…

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Q: 11. Use the Shell Method to calculate the volume V of the solid obtained by rotating the region…

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Q: 1 3) Consider the region bounded by the graphs of y =-x, y= V4-x , and y=0. 3 c) If this region is…

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Q: Consider the region enclosed by the curves y = x²+1 and y = 2x + 1: 5- The volume of the solid…

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Q: (4) Find the volume of the solid obtained by rotating the region bounded by y y=√x about the y = 1.…

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Q: 1. Find the volume of the solid that lies under the paraboloid z = x² + y² and above the region…

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Q: 46. Find the volume of the solid produced by rotating the region enclosed line y = -1 that is…

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Q: 1. Use your preferred method to calculate the volume of the solid obtained by revolving the region…

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Q: 3) Find the volume of the solid created by revolving y = x2 around the x-axis from x = 0 to x = 1

A: Given the given curves are y=x2x=0x=1 Method Use disc method to find the volume of revolution of the…

Q: 4) (6.) Find the volume of the solid formed from the region between y = e*, y = 0, x = 0, x = 1…

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Q: Consider the region bounded by the graph of y2 = (4-x)^2/(1+x)^2 on the interval [0, 1]. Find the…

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Q: 4 8. What is the volume of the solid generated when the region bounded by y= V4 +3x – x and y = 2 is…

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Q: 6. Find the volume of the solid obtained when the region bounded by y ==, y = 0,x = 1, and x = 2 is…

A: As per the our guideline, we are supposed to solve only first question. Kindly repost other question…

Q: 4. Find the volume of the solid obtained by rotating the region bounded by y = e", y = 0, x = -1, x…

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Q: 15. Find the volume of the solid obtained by rotating the region bounded by xy = 4 and y = (x – 3)…

A: Given :  xy=4  and  y=x-32. Therefore, x-32=4x⇒xx2-6x+9=4⇒x3-6x2+9x-4=0⇒x-12x-4=0Therefore, x=1 ,…

Q: 6) Use the washer method to find the volume of the solid generated by revolving the region y = x² +1…

A: We first sketch the region using a graphing calculator. From the graph, we see that x is from 0 to…