Find the volume of the solid obtained by rotating the region bounded by y= 54x-6x2 and y= 0 about the y-axis.

Q: Calculate the volume of the solid obtained by rotating the region bounded by y = x 2 – 4x + 5, x =…

A: Topic - application of integration

Q: Compute the volume of the solid obtained by revolving the graph of y =1+x^2/2 on [0,1] about the…

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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 obtained by rotating about the y-axis the region bounded by y = 2x² -…

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Q: Find the volume of the solid formed by revolving the region bounded by y = (x – 2)2 and y = x about…

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Q: Find the volume of the solid generated when the region enclosed by y = \2x + 8, y = x, x = 0 is…

A: If y=f(x) is a function, then the independent variable x is called the input of the function, and…

Q: Find the volume of the solid obtained by rotating the region bounded by y = x2 + 2 and y = 4 - x²…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by x = -3 + y² and x = -2y…

A: Given the curve is x=-3+y2, x=-2y Outer radius=-3+y2+9=y2+6 inner radius=-2y+9 Intersection point is…

Q: Find the volume of the solid formed by revolving the region bounded by the graphs y = √x and y = x^2…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = x² + 2 and y = 4 - x²…

A: Solution:-

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

A: We will find the volume of revolution as following.

Q: Find the volume of the solid generated when the region bounded by y = 9 – x and y = 2x + 6 is…

A: To find the volume of solid generated by revolving around the x axis

Q: Find the volume of the solid generated when the region bounded by y= 9x and y 27x is revolved about…

A: Given curves are y=9x   ....1 and y=27x  ...2

Q: Find the volume of the solid obtained by rotating the region bounded by y = 3x², x = 2, x = 5 and y…

A: Topic- application of integration

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

A: The region to be rotated and the limits will be as follows.

Q: Find the volume of the solid obtained by rotating the region bounded by the curves y = x 2 – 3x + 2,…

A:

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

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Q: Find the volume of the solid obtained when the region bounded by the x-axis, the y-axis, and the…

A: We have to find volume of the solid bounded by given region

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: 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 obtained by rotating the region bounded by y = 7x², x = = 1, and y = 0,…

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

A: This question is based on application of Integration.

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

A: Given : The curves y=x2+4x+5  , y = 0.   To determine : The volume of the solid obtained by rotating…

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

A: we know that formula for volume of revoution about x-axis is Volume=π∫abf2(x) dxf(x) =1-x2(a,b) =…

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

A:

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 obtained by rotating the region bounded by y=x^2-4x+5,x=4 , and…

A: volume of the solid of revolution about x axis of a curve y=fx, from x = a to x = b is given by…

Q: Find the volume of the solid obtained by rotating the region bounded by  y = 35x − 7x2  about the…

A:

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: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y=x^3, y=8, and x=0 about…

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Q: Determine the volume of the solid obtained by rotating the region bounded by y = 2vx – 1 and y =x-1…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by the curves: x=0 and…

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

A:

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

A: Below is the solution to the question:-

Q: Find the volume of the Solid generated by revolving the region bounded by y = -2x² and y = x² – 3 ,…

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Q: find the volume of the solid obtained by revolving the region bounded by y = x - x2 and the x - axis…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y = 4x², x = 1, and y = 0,…

A:

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 the solid obtained by rotating the region bounded by y = 4x², x = 1, and y = 0,…

A:

Q: Find the volume of the solid formed by rotating the region enclosed by 5x Y = e + 4, y 0, 0, = 0.9 ,…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by x = 8 – y² - and x 2y about…

A: Given the region is bounded by the curves x=2y and x=8-y2 about the line x=9. The curves intersect…

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 obtained by rotating the region bounded, by y x2 - 2x and y = x about…

A: The region bounded by the curves y=x2-2x and y=x about the line y=4 is as shown above.

Q: Find the volume of the solid obtained by rotating the region bounded by y 5x-x2 and y-x about the…

A:

Q: Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 2x² -…

A: Solution of given question is written in below steps.

Q: Find the volume of the solid obtained by rotating the region bounded by -6+ y² and x = y about the…

A:

Q: Find the volume of the solid obtained by rotating the region enclosed by the curves y = x2 + 2 and y…

A:

Q: Find the volume of the solid generated by revolving the region bounded by y = 3x – x² and y x2 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.