Find the volume of solid generated by revolving the area bounded by y³=x, y=2 and x=0 about the x-axis.

Q: Find the volume of the solid of revolution generated by revolving the region bounded by x = 1, x =…

A: Consider the graph:

Q: Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and…

A: Given

Q: Find the volume generated by revolving the region bounded by y=−x^4+3x^3, y=0  revolving about the x…

A: The given problem is to find the volume generated by revolving the region bounded by given curves…

Q: Find the volume of solid generated by revolving te area enclosed by : x=y²+1, x=0,y=0 and y=2 about:

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Q: Determine the volume of the solid formed by revolving the area bounded by x2 = 4y– 4, x= - 2, x=3…

A: Given region R is bounded by x2=4y-4x=-3x=3 Region R is shown below

Q: Determine the volume of the solid formed by revolving the area bounded by X = 4y-y and y=X about the…

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Q: Find the volume of the solid generated by revolving the region bounded by y=6x−x^2 and y=0 about the…

A: Given : region is bounded by y=6x-x2 and y=0 To find : volume of the solid generated by revolving…

Q: Find the volume of the solid created by revolving the bounded region created by the graphs of y = Vx…

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Q: Determine the volume of the solid formed by revolving the area bounded by y= x, y=0 and x= 3 about…

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Q: Find the volume of the solid obtained by revolving the region bounded by y = In x, y = -8, and x = 7…

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Q: Find the volume of the solid formed by rotating the region enclosed by 4x y = e about the x-axis. +…

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Q: Find the volume of the solid formed by revolving the region bounded by y = x – a° and the x-axis (0…

A: The region bounded by x = f(y) and the y‐axis on [ a, b] is revolved about the y‐axis, then its…

Q: Find the volume of the solid generated by revolving about the x-axis the area bounded by y=v(x),…

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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 formed by revolving the region bounded by y = sin 2x, x = 0, and x =…

A: We need to find the volume of solid formed by revolving the region bounded by the curve about the…

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: Determine the volume of the solid formed by revolving the area bounded by y= x- 2x and y=0 about the…

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x)and the x−axis…

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: As per the guidelines i am solving first question. 1. Consider the given curves, y=x2, x=3 and y=0.…

Q: Determine the volume of the solid formed by revolving the area bounded by X+y-6 = 0, y=3 and x=0…

A: The solid formed by revolving the area bounded by x+y-6=0, y=3 and x=0 about the y-axis.

Q: Find the volume of solid generated by revolving the region bounded by the lines y = 0, x = 2 and…

A: We have to find the volume of solid bounded by given region revolving around X-axis.

Q: Find the volume of the solid generated by revolving the region bounded by the curves y = 1- jx| and…

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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 of the solid generated by revolving the region bounded by y=sqrt x, y=-1/2x+4, x=0,…

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Q: Find the volume of the solid generated by revolving the region bounded by the line y = 0 and curve y…

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Q: Find the volume of the solid generated by revolving about the line x = 2, the area bounded by y =…

A: The equation of the curves are  C1: y = x2C2: x= 2C3: y = 0 The axis of the revolution is x = 2 To…

Q: Find the volume of the solid formed by revolving the region bounded by y=6x−x2,y=0 about the x-axis

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Q: Find the volume of the solid that results when the region enclosed by 4x 0, x = 1, and y = 0 is…

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Q: Find the volume of the solid generated when the region enclosed by y = root(x+3), y = root(3x+1),…

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Q: . Find the volume of the solid generated by revolving the region bounded by y = vx-1, y = 0 and the…

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Q: Find the volume of the solid generated by revolving 67 from y = 1 to y= 2 about the y-axis.

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Q: Find the volume of the solid generated by revolving about the x-axis the area bounded by y=√(x), x=4…

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Q: Find the volume of the solid generated by revolving the region bounded by y = 2x, y= 0, x= 0, and x=…

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Q: Find the volume of the solid generated by revolving the region bounded by the curves y=x and y=4x –…

A: TTt

Q: Determine the volume of the solid formed by revolving the area bounded by y= X² and x=y² about the…

A: The formula for the volume of the solid formed by revolving the region bounded by the curves, y=f(x)…

Q: Find the volume of the solid obtained by revolving the region bounded by y=x and y=x^2 about x-axis

A: Given: The region between the curve y=x and y=x^2   The volume of the region revolving about the…

Q: Find the volume of the solid generated by revolving the region enclosed by y=(x+1)2 , y=-x+5, and…

A: Given

Q: Find the volume of the solid generated by revolving the region bounded by y = x² – 2x + 2 and y = x…

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

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Q: Find the volume of the solid of revolution generated by revolving y = 9-x from x= - 3 to x= 3 about…

A: Given f(x)= 9-x2    where -3≤x≤3 To find the volume of the solid of revolution here use The Disc…

Q: Find the volume of the solid generated by revolving the region bounded by x=1+ y^2 and y=x-3 about…

A: Given: Region is bounded by the curves, x=1+y2 y=x-3 Objective of the question is to find the volume…

Q: Find the volume of the solid generated by revolving about the x-axis the area bounded by y = vx, x=…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of y=2x2+1 and…

A: First draw the both curve and find the region which will be rotated about x-axis.than use disc…

Q: Find the volume of solid generated by revolving the area bounded by y = 8x and y = 2x about y=4.

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Q: Find the volume of the solid generated by revolving the region bounded by y = 4/T , y=4, and x=0…

A: The volume made by full revolution in the area between the curves y1=f1(x) and y2=f2(x) where…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of y = x3 , x =…

A: Given curve: y= x3 At x=2, y =8 At x=0, y=0 We know that  The volume of the solid formed by…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of y = x3 , x =…

A: Topic = Application of integration

Q: Find the volume of solid formed by revolving region by f(x)=x^(2/3), x=0, y=0, y=1 about the y-axis.

A: Given:

Q: Find the volume of the solid obtained by revolving the area enclosed by y = 2x, y = 2 and r = 0…

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Q: Find the volume generated by revolving the area bounded by the parabolic arc Vx + Jy = Va and the…

A: Given problem:- Find the volume generated by revolving the area bounded by the parabolic arc √x + √y…

Q: Find the volume of the solid generated by revolving the region bounded by y = x³,y = 0, x = 2 about…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.