Find the volume of solid by y=x^2 and y=x^3 about the y-axis using washer method and shell method.

Q: Find the volume of the solid generated by revolving the region by graph of function f(x) 10 ;x 1.25,…

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Q: Find the volume of the solid generated by revolving the region in the first quadrant bounded by the…

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Q: Find the volume of the solid generated by revolving the region bounded by y=x+3, y=4 and x=5 about…

A: We first sketch the region using a graphing calculator  The shaded region is rotating about the…

Q: Find the volume of the solid formed by revolving the region bounded by f(x) = Vx, y = 0, x = 3 about…

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Q: Find the volume of the solid obtained by rotating the curve y=x^2 , y= square root x , the lines x=0…

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Q: Find the volume of the solid formed by rotating the region bounded by y = 5 – 2x, y =x² and x > 0,…

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Q: Find the Volume of the solid obtained by rotating the curve 1 for 1 < x < 4 1+ x2 around the line r…

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Q: Find the volume of the solid of revolution formed by rotating the area under y=9-x2 over [0, 3]…

A: Given curve is y=9-x2 ,[0,3]

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 region in the first quadrant bounded above…

A: Here the given problem is about finding volume of solid generated by revolving the region in first…

Q: Find the volume of the solid obtained by rotating the region bounded by y = −10+ 6x - x², x = 1 and…

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Q: Find the volume of the solid obtained when the region under the curve y = xV4-x2,0 < x < 2 is…

A: The volume of solid revolution V=∫abπfx2-gx2dx fx=x4-x2 where, a=0 and b=2

Q: : Find the center of mass of a thin plate of constant density covering the region bonded by y = 25 -…

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Q: find volume of solid 3x^2 ,x=1, y=0 about x axis

A: Consider the region bounded by the curves y=3x2,x=1,y=0 as shown in the figure below: Here, the…

Q: ) Find the volume of the solid formed by revolving the region bounded by the cu y = √9-x² and y = 0…

A: To Find:  Volume of the solid formed by revolving the region bounded by the curve       y = 9 - x2 ,…

Q: To find the volume of the solid generated by revolving the area bounded by the given curve about the…

A: The volume of the solid generated by revolving the area bounded by the curves f(x) and g(x) over the…

Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y 1, and the…

A: Here, to find the volume of the solid whose base is the region in the first quadrant bounded by…

Q: Find the volume generated by revolving the area bounded by y = x3 – x2 , x-axis, about y-axis by…

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Q: Find the volume of the solid formed by revolving the region bounded by the curves y = 3x²,x = 0, and…

A: Given : Curves y = 3x2, x = 0 and y = 3   To find : Volume of solid formed by revolving the region…

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 obtained by rotating the region bounded by y = 56x – 8x² and y = 0…

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Q: What is the volume obtained by revolving the are biunded between the lines y=x, y=2x and x=4   about…

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Q: Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 25 about the line y…

A: Explained below

Q: Find the volume of the solid generated when the area bounded by the curve y^2=x, x-axis and the line…

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Q: Find the volume of the the solid formed by revolving the region bounded by y=5-x; y=0; about the…

A: Integration of function expression with respect to variable x or y gives the area between function…

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

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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 formed when the region bounded above by the curve y =sqrt( x +1), y = 1…

A: We need to first plot all the equations given to us to roughly understand the region being talked…

Q: Find the volume of the solid generated by revolving the curve y=3vx between x = 0 & x = 3 about the…

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Q: : Find the volume of the solid generated by revolving the shaded region about the x-axis: y = sinx…

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Q: Find the volume of the solid formed by revolving the region bounded by y=1/2x^3, y=0, and x=3 about…

A: Given:

Q: Use cylinder shell method to graph and find volume: y=sqrt(x), y=0, x=1, about x=-1

A: If a region is bounded by a curve y=fx and x-axis on the interval a,b and it is rotating about a…

Q: Find the volume of the solid generated by revolving the region bounded by the y = 4x - x2 and y = 0…

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Q: When we calculate the volume of solid obtained by rotating the region bounded by the curves y = 2x²…

A: Given:       Curves y=2x2                   y=2x and line y=2 Volume of solid V=π∫abfx2-gx2dx

Q: The area bounded by the line x=1 and the curve y^2-x=3 is revolved about the line y=4. Using Shell…

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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 formed by revolving the region bonded by the graphs of y = x + 2, y =…

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

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Q: Find the volume of the solid whose base is the region enclosed between the curve x = 1−y² and the…

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

A: The graph of the region is shown below:

Q: Find the volume of the solid generated of the area bounded by y = x², y + 2x = 8 and y = 0, rotat…

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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 formed by rotating the region enclosed by 5x Y = e + 4, y 0, 0, = 0.9 ,…

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Q: Find the volume of the solid. y=9-x2, y=0, about the x-axis

A: The given solid is bounded between the curve y=9-x2, y=0,  rotating about the x-axis. Volume of the…

Q: Find the volume of the solidgeneruted by revolving the region between the x-axis and the curve…

A: We first find where y=x2-2x and x-axis meets.x-axis means y=0.So, 0=x2-2xor, 0=x(x-2)or, x=0, 2 The…

Q: Find the volume of the solid formed by rotating the region bounded by y = ² and y = x-axis using the…

A: Washer method

Q: Find the volume of the solid generated by revolving the region between the y-axis and the curve x =…

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Q: Find the volume of the solid generated by revolving the shaded region about the y-axis. y 3

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

A: Given query is to find the volume generated for the given curve.

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.