Calculate the volume calculated by rotating f(x) = x2 for x ∈ [1,3] about the axis of the x.

Q: Find the volume of the solid obtained by rotating the region under the graph of the function…

A: We first sketch the region using a graphing calculator  The shaded region will rotate about the…

Q: Find the volume of the solid generated by the area bounded by the curve y = x³,x = 1,x = 2 and y = x…

A: The volume of a region is the integration of the area of the region. It can be calculated using…

Q: Find the volume of the solid of revolution bounded by y = 1/(x+1), x = 0, x = 2, and the x-axis, and…

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Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

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Q: Find the volume generated by the area bounded by the parabola x = Vay , and the line y = b that is…

A: As per our guidelines, we are suppose to answer only one question. kindly repost the question as the…

Q: The volume generated when ℝ is rotated about the x-axis.

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Q: Find the volume generated by rotating the region between the graphs of x = sqrt (y) , x = 0, and y =…

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Q: Find the volume generated by revolving the area bounded by y = 1 - x³, OX and OY about the x-axis.

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Q: Find the volume of the solid. y=x2, x=0; x=2, y=0, about the x-axis

A: use the volume of solid of revolution formula,

Q: Find the volume of the solid generated by revolving the area bounded by x- y2 + 6y-9 0 and x- y-9 =…

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Q: Find the volume of the solid generated when the region enclosed by y = -√√x + 1, y = 0, and x = = 2…

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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 swept out by revolving the region bounded by the y-axis and the graph of x = t (1 -…

A: Given,

Q: Find the volume of the solid generated by the curve f(x)=4-cosx revolved 360° about the x- axis in…

A: We calculate the required volume using integration. ∫4-cos x2dx=∫16-8 cos x + cos2 xdx=∫16-8 cos x…

Q: Find the surface area of the volume generated when of y = x3, on the interval [0, 1], is revolved…

A: We have to find the surface area of the volume generated by the curve by rotating about the y axis.

Q: Find the volume of the solid generated by revolving the area bounded by x - y² + 6y - 9 = 0 and x -…

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Q: Find the volume obtained by rotating f(x) = x(1 – x) around the x-axis.

A: Given             f(x)=x(1-x) and y=0

Q: Find the volume between the cylinders x+y =1 and the cylinder x* +z* = 1 in the first octant. 2

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Q: Compute the volume of the solid obtained by revolving the graph of the function f(x) = 6x^5 on the…

A: Given fx=6x5 rotated about x axis in the interval x=-2 , x=+2Find volume generated .

Q: Find the volume of a solid of revolution formed by revolving the region bounded by the graphs of…

A: The objective is to find the volume of a solid generated by revolving the region bounded by the…

Q: Find the volume of the solid obtained by rotating the region under the graph of f (x) = 9 − x2 for 0…

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Q: Find the volume of the solid formed by y = 4 sin(x) bounded by x = 0 revolved about the x axis on…

A: We have to find the volume of the solid formed by y=4sinx bounded by x=0 revolved about the x axis…

Q: Find the volume of the solid which is (a) bounded by x+ y+z = 4 in the first octant.

A: As per our guidelines we are supposed to solve only one question. For the solution follow the next…

Q: Find the volume of the solid obtained by rotating the region under the graph of the function f(x) =…

A: We will  use concept of integration to solve this. In particular disc method  will be used.

Q: Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 16 about the y-axis

A: Given Data: Curve: x2+y2=16   The figure below indicates the graph of the curve.   The intersection…

Q: Find the volume generated when the area bounded by the two curves of x^2 = 4y and y^2 = 4x is…

A: We will find out volume of solid of revolution.

Q: Find the volume generated by rotating the region bounded by y = x, x = 1, and y2 = 4x, about the…

A: Here we solve the integral problem.

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: Find the volume generated by revolving the area bounded by xy=4, x=1, x=4 and the x-axis about the…

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Q: Find the volume of the solid obtained by rotating the region under the graph of the function f(x) =…

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Q: Find the volume generated by revolving the area bounded by y² - 4y - 4x + 4 = 0 and x = 1 about the…

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Q: The integral for the volume of the solid obtatned by rotating the regton bounded by the curves y =…

A: Volume is 2πe where e is exponential.

Q: Find the volume bounded by the cylinder x² + y² = 9 and the planes y + z = 4, z = 0, using double…

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Q: 3. Find the volume when the part of the curve y = x + 1 between x = 1 and x = 2 is rotated through…

A: Here we have to find the volume when the part of the curve y=x2+1 between x=1 and x=2 is rotated…

Q: Compute the volume of the solid obtained by revolving the graph of the function f(x) = 7x^5 on the…

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Q: Find the volume of the solid generated when the region bounded by y = x2and y2 = x is revolved about…

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Q: Consider rotating "R" about the x-axis to form a solid of revolution. When we integrate to find the…

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Q: Find the volume of the solid obtained by rotating the region under the graph of the function…

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Q: Find the volume of the solid of revolution that results when the region under the graph of…

A: For radius = x , height = f(x)= e^-x

Q: Find the volume generated by revolving the area bounded by y² - 4y - 4x + 4 = 0 and x = 1 about the…

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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: Find the Volume y=0, y= 1/x, x=1, x=4 revolving at the x-axis

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Q: Compute the volume of the solid formed by rotating the region bounded by the given functions about…

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Q: What is the exact volume of a solid that is formed by rotating the region, enclosed by the functions…

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Q: Calculate the volume of the solid of revolution generated by rotating the graph of the following…

A: Given: The function is fx=1x. To find: Volume of the solid in the interval x∈1,2. Concept used:…

Q: Find the volume of the solid obtained by rotating the region under the graph of the function…

A: volume is 76.9858 detailed solution with explanation is given below

Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y = -2 about the…

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Q: Find the volume of the solid formed f(x) Vx, y = 0, X = %3D about the x-axis.

A: Here we have to find the Volume of the solid formed by revolving  the region bounded by,  f(x)=√(x),…

Q: Use integration to find the volume of the solid that lies within the cylinder + y= 4, below the cone…

A: We will find out the required volume.

Q: The integral represents the volume of a solid of revolution. 2T X° dx

A: Use the principle of integration to evaluate the given problem.