Write the Integral(s) for the VOLUME generated by revolving the region bounded by: y = x?, y = 12 –- x, x = 0, around line y = -2

Q: Find the volume of the solid generated by revolving the specified region about the given line. R…

A: Given  the graph in the question  from the graph outer radius R(y) is y = x and the inner radius of…

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: Identify the definite integral that computes the volume of the solid generated by revolving the…

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: A/ Find the volume generated by revolving the area bounded by x = y-1 and y =5 around the x-axis?

A: We will find out the volume of solid of revolution by shell method.

Q: Find the volume obtained by rotating the bounded region defined by y = Vx y = 0 , and x = 4 around…

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

A: Given data: The given equation of the line is y=-x+6. The given limits of x are [a, b]=[0, 6]. The…

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: Find the volume generated by rotating the given region about the specified line. R about y = 0

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: . Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

A: Here we use the basic form of revolution of curve around X axis

Q: Sketch the area bounded by x^2 + 2y = 4 and x + y + 2 = 0 on the image below and determine the…

A: volume of above function is π×175.19 cube unit

Q: What is the volume obtained by rotating the region bounded by x = (y - 3)½ and y = 2x2 + 1 around…

A: Here we use basic definition of volume .

Q: The volume generated by revolving the area bounded by the curve y = x² and y = 4 around the line y =…

A: We can use the formula π∫abR(x)2dx to evaluate the volume.

Q: Find the volume generated by revolving the area bounded by y=ex, x=0 and y=0 about the y-axis.

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Q: Find the volume generated by the region bounded by - y = z, z= 0 and y = 1 when it is revolved about…

A: The region is bounded by y2=x , x=0 and y=1 as :-

Q: Set up the integral that gives the volume of the solid formed by revolving the region bounded in the…

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Q: Find the volume generated if the area bounded by the curve x² = y – 2 is revolved about the x-axis.

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Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 4x + 8y = 8,…

A: We need to find volume.

Q: Find the volume generated by revolving the area bounded by y = x? – 2x + 3, and y = 3 about the line…

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Q: Find the volume of the solid generated by revolving the area bounded by x? – 2kx – 2ky + k² = 0 and…

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: generated

A: We have to find the volume  according to the given information

Q: Set up the integral that represent the volume of the solid obtained by rotating the region bounded…

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Q: Sketch the area bounded by x^2 + 2y = 4 and x + y + 2 = 0 on the image below and determine the…

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Q: Compute the volume of the solid formed by revolving the given region about the given line. Region…

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Q: Determine the volume obtained by rotating the area enclosed by y = x(4 – x) and y 0 about the line x…

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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 y² – 4y – 4x + 4 = 0 and x = 1 about the…

A: Volume bounded by the region along x=1

Q: Find a single integral whose value is the volume of the solid obtained by rotating the region…

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Q: Determine the integral that represents volume bounded by z--1, z- 2, y - 0 and y- + 2

A: Given x=-1,x=2,y=0,y=12x2+2

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 volume generated by rotating the given region about the specified line. R about y =0

A: Do integration to find the area between two curve.

Q: Find the volume generated by revolving the area bounded by the given curve and a. y = x³, x = 0, y =…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Area bounded by y2 = x and x – y – 2 = 0, revolve about x = -1

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Q: Set up the integrals to find the volume generated by revolving the region bounded by y 4 – 2x and y…

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Q: Set up the integrals to find the volume generated by revolving the region bounded by y = 4 – 2x and…

A: here is the solution

Q: Find the volume generated by revolving the area bounded by y² – 4y – 4x + 4 = 0 and x 1 %3| about…

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Q: Find the volume generated if the area bounded by the curve x? = y – 2 is revolved about the x- axis.

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Q: Find the volume generated by revolving the area bounded by x2 – 4x – 4y + 4 = 0 and y = 1 about the…

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: find the volume generated by revolving the area bounded by y = x^2 - 2x + 3 and y = 3 about the line…

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Q: Find the volume generated by revolving the area bounded by : 2, x = 5, and Ж — x3 + 9x² + 18x y = 0…

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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 obtained by rotating the region bounded by x = y^2 and x = y around the x-axis.

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Q: Set up and evaluate the integral that gives.the volume of the solid formed by revolving the region…

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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.