Sketch the region bounded by the curves y=x, y=−x+ 4 and y= 1. Set up, but do not evaluate, integrals to find the volume of the solid obtained by rotating about the following lines: vertical line x=4(Make sure to show pictures of disks, washers and/or shells as part of your work.)

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

A: Given: y=x4y=0,x=1

Q: Find the volume of the solid that results when the region bounded by x = y and x = y + 12 is…

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Q: Sketch the region bounded by the graphs of y = x² +1 and y = x +1. Then use the method of shell to…

A: We sketch the region using a graphing calculator  The shaded region is rotating about the x=2 line…

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

Q: Find the volume of the solid obtained when the region bounded by the curves y = x^4 − 2x and y = 0…

A: We have to find the volume of of the solid of revolution of the region bounded by the curves y=x4-2x…

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: Set up the integral to find the volume of the solid obtained when rotating the regionbounded by…

A: Given: y = x3,  x =0,  y=2,  y = 11 To set up: The integral to find the volume of the solid obtained…

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: y = yx, y= 1, x=4; about the line x = 5.

A: Given that: y=x, y=1,x=4 about the line x=5

Q: Set up the integral that will give the volume of the solid generated when the region bounded by the…

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Q: . Find the volume of the solid obtained by rotating the region bounded by  y = √x    x = 0, and x =…

A: Given curve y=x, x=0 and x=4. The volume is generated by curve rotating about x-axis.

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

A: From the given region: Apply the disc method to find the volume about the x-axis. The area of the…

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

A: Volume between curves about y=d.

Q: Sketch the region bounded by the curves y = 6 vx and y = 6x then set up the integral needed to find…

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Q: Set up an integral that represents the volume of the solid obtained by rotating the region enclosed…

A: We have to set up integral that represents the volume.

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

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Q: Consider the region enclosed by y=x2 , the y-axis, and y=1. Set up the integral of the volume of the…

A: Here is the solution of the given problem:  Washers Method:  Cylindrical Method::

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

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Q: The integral that represent the volume of the solid obtained by rotating the region bounded by y =…

A: We will find the volume as following.

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 of the solid obtained by rotating the region bounded by the given curves about the…

A: Shell Method:- Shell integration is a method for calculating the volume of a solid of revolution,…

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 area in the first quadrant bounded by y = x^2,…

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

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Q: Consider the region bounded by the curves y = √x, x = 4 and the x −axis. 1. Set-up only the…

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

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Q: Set up the integral that will give the volume of the solid generated when the region bounded by the…

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Q: Set up the integral that will give the volume of the solid generated when the region bounde che…

A: We are asked to setup the volume of the integral.

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 the given curves 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…

A: The given curve is: y=9-x2

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

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

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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 that results when the region enclosed by y= \x, y=0, and x =9 is…

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Q: Find the volume of the solid obtained by rotating the region bounded by y=x and y=xl/2) about the…

A: Solution:Giveny=x and y=x12To find the Volume of the solidFormula:V=2π∫abR(x)h(x)dx

Q: y = Vx + 1 + x and the x-axis from x = 0 to x = 3 about the y-axis.

A: When rotating about y axis, we should use shell method to find the volume. The formula for volume is…

Q: Set up the integral that will give the volume of the solid generated when the region bounded by the…

A: The integral can be modelled by calculating the intersection points of the curves. The intersection…

Q: Set up the integral that will give the volume of the solid generated when the region bounded by the…

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Q: Set up the integral that will give the volume of the solid generated when the region bounded by the…

A: Set up the integral that will give the volume of the solid generated when the region bounded by the…

Q: Set up the integral that you would need to solve to find the volume of the solid created by rotating…

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Q: x = 1 – y*, x = 0; about x = 5. Volumo

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Q: Set up the integral to find the volume of the solid obtained when rotating the region bounded by y =…

A: To set up the integral for finding the volume of the solid obtainedwhen rotating the region bounded…

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

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Q: Find the volume of the solid that results when the region bounded by y = x and y = x², from x = 0 to…

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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.