3. Determine the volume of the solid obtained by rotating the region bounded by y = 2vx – 1 and y = x-1 about the line x = -1

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

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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: Ex/ Find the volume of solid generated by revolving the region y2 and x = y enclosed by x = 1- about…

A: You have posted multiple question. As per the instruction, we will be answering the first question.…

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: 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 of the solid under the paraboloid z = 4–x²–y² and over the region x²+y² < 1.

A: We have to find the volume of the solid.

Q: 7. Find the volume of the solid obtained by rotating the region bounded by and r = 0 about the…

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

A: Given:

Q: SI xyz dW, B is region bounded by two cylinders, wwwm w В x^2 + y^2 = 16, x^2 + z^2 = 16, and the…

A: Consider the given volume of the two intersecting cylinders given by  x2+y2=16 andx2+z2=16  as shown…

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: 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 of the solid obtained by revolving the region under y = ex for 0 ≤ x ≤ 2 about the…

A: The radius of the region= x Height = y= ex

Q: 3. Consider the region bounded by the y-axis, y = V3x + 1, and r = 4. Set up an integral to compute…

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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: 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 generated by rotating the region bounded by the curves y = Vx y = x…

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Q: 3. Consider the region bounded by y = 5 - x 2, y = x - 1, and x = 1. Set up an integral to find the…

A: Concept Used: (Shell method) The Volume of the solid obtain by the rotating the region is given by…

Q: Find the volume of the solid formed by rotating the region bouned by y=x and y=xln(x) around x=-1

A: Consider the provided curve, y=x  and  y=xlnx Find the volume of the solid formed by rotating the…

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

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Q: Let A be the region bounded by y = 8x 3(1−x) and the x-axis between x= 0 and x= 1. Find the solid…

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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: 1. Use the method of shells to find the volume of the solid generated when the r bounded by x= Jy ,…

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

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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: Find the volume of the given solid. Under the surface z = 1 + x²y2 and above the region enclosed by…

A: To find the volume of the given solid.

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: nd the volume of the solid generated when the region bounded by y = x² - x d y = x – x² is revolved…

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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: Let a> 1 be a constant and let R be the region bounded by y= 6x² and y = 6x + 12 . Find the volume…

A: Given: Region bounded by y = 6x2 and y=6x+12 To find: volume of solid generated  by revolving region…

Q: 12. Set up an integral to find the volume of the solid generated when the vegion bounded by y=…

A: Giveny=x  , y=o , x=4

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

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Q: Find the exact volume of the solid whose region is bounded by y = 2 a + 2, y = 0, x = 3 and x =…

A: Given data : y=2x+2 , y=0x=3 , x=4

Q: 23. Find the volume of the solid formed by the region in the first quadrant bounded by: x = y - y, x…

A: *to find:- Volume of revolution of solid.

Q: Let a> 1 be a constant and let R be the region bounded by y = 6x2 and y = 6x + 12. Find the volume…

A: Given y=6x2, y=6x+12

Q: Calculate the volume of the infinite solid obtained by rotating the region under y = (x2 + 1) −2 for…

A: Use shell method and find the volume.

Q: find the volume of the solid generated by rotating the indicated region about the given line: y=x2,…

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Q: Find the volume of the given solid. Under the surface z = 1 + x²y2 and above the region enclosed by…

A:

Q: Find the volume V of the solid of revolution that results when the region under the graph of f(x) =…

A: To find the Volume V.  Given that f(x) = ln(x).

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: and a) x = y² + 1₁ x = 0, y =- y = 2 The volume generated by revolving the region about the line y=2…

A: We can solve as follows

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 ,…