1. vetermine the volume of the solid obtained by rotating the region bounded by the curves y = x2 – 2x and y = x about the line y = 4.

Q: The graph of the volume for solid revolution between the curves y = x+1 and y = O around the x -…

A: Plot the lines and determine the area bounded by these lines. Use the area and the rotation about…

Q: 2. Determine the volume of the solid obtained by rotating the region bounded by y = 4x and y = x³…

A: The volume of revolution of the area bounded by the curves y1=f1(x) and y2=f2(x)  between the limits…

Q: b) [ Find the volume of the solid obtained by rotating the region bounded by the curve about the…

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Q: d the volume V of the solid obtained by rotating the region bounded by the ren curves about the…

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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: The volume of the solid generated by revolving the region between the parabola x =y²+1 and the line…

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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: 6. Evaluate the volume generated by revolving the area bounded by the given curves using the washer…

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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: 16. Find the volume of the solid generated by revolving the region enclosed by y = 3sinx and y = 0…

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Q: 1. Consider the region bounded by y = x and y = vVa, shown below. Find the volume of the solid…

A: Volume=13π15 cubic units

Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y- axes. If the region is revolved…

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Q: 5. Find the volume generated by revolving the area under the curve y = e from x = 0 to x = 1 (a)…

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Q: 1) Calculate the volume of the solid created by rotating the region bounded by y = x² +1 y = -x + 3…

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Q: 3. Find the volume of the solid whose base is the region in the first quadrant between the curve y=…

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

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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: 1. Find the volume of the solid obtained by rotating the region bounded by the given curves about…

A: Proceed as shown below

Q: Find the volume using the disk or washer method

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

Q: ind the exact volume of the solid generated by revolving the region bounded by the given curves…

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Q: b) : Find the volume of the solid obtained by rotating the region bounded by the curve y = -x² + 11…

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Q: 6. Consider the region created by revolving y = 4 +x, y = 3 – x, x = 0, and x = 2 about the y -axis.…

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Q: 1. Consider the region bounded by y = x and y = Vx, shown below. Y Find the volume of the solid…

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Q: Find the volume V obtained by revolving the region between y = x2 + 4 and y = 2 about the x-axis for…

A: To find: The volume V obtained by revolving the region between y = x2 + 4 and y = 2 about the x-axis…

Q: Rotate the region specified above by the curve y = x and beneath by the curve y = x2 from x = 5 to x…

A: Explained below

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: The region R bounded by y=x^(1/2) +2 and y=x2+2 in the first quadrant is revolved about the line…

A: The given equations are

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

A:

Q: and y=2 8) x = y² +1₁ x = 0, you, The most appropriate method to use to find the volume generated by…

A: The given region is x=y2+1,x=0,y=-1 and y=2. Find the volume generated by revolving the region about…

Q: 1. Consider the region bounded by y = x and y = √ x, shown below. x y Find the volume of the solid…

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Q: 18. The integral that represents the volume of the solid obtained by rotating the region bounded by…

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Q: Let a> 1 be a constant and let R be the region bounded by y = 20x2 and y = 20x + 40. Find the volume…

A: Consider the given functions. y=20x2 and y=20x+40 Put both functions equally.…

Q: 3. y = 1-x ve x +y 1 Calculate the volume of the rotational turf formed 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: 1- Find the volume of the solid obtained by rotating the region bounded by the curve y = 4 - r and…

A: The volume of the solid of the revolution of the curve y=f(x) obtained is  Volume=∫abA(x)dx  or…

Q: 12. Consider the region R bounded by the line y = 37 – 7x and the parabola y = 27 – x² . %3D Find…

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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: 2. Consider the region bounded by the y-axis, y = 3x+ 1, and r 4. Find the volume of the solid…

A: Given function are y=3x+1x=4y axisAxis of rotation y=-5

Q: Consider the reg. A enclosed by the curves y = x2 +1 and y = 2x + 1: 2 The volume of the solid…

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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 on the 1st quadrant bounded by y = √4x²,x and y-axes. If the region is revolved…

A: This is a problem of the volume of rotation

Q: 4. Calculate the volume of the solid under the plane 4x + 2y – z = 0 and above the finite region R…

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Q: Rotate the region specified above by the curve y = x and beneath by the curve y = x^2 from x = 0 to…

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Q: 9. Find the volume of the solid generated by revolving the region bounded by the lines and curves y…

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Q: Find the volume (in cubic units) of the region bounded by the curves y = sin x ,and y = cos x and…

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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 ,…