The volume generated by revolving the area bounded by the curve y = x² and y = 4 around the line y = 4 is 512 15 True False

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: What is the volume of a solid object formed by rotating the region between f (x) =6x² + 3 and g (x)…

A: Let the region bounded by the curves fx=6x2+3 and gx=4x2-3 be R.  R is rotated about the line y=-3…

Q: 5. Find the volume generated by revolving the region bounded by y = 9- x2 and y = 0 about the…

A: Given: The region bounded by y=9-x2 and y=0 is revolved around x axis. Let the bounded region be R.…

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: 6. What is the volume generated when the area in the first quadrant bounded by the curve x? = 8y,…

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Q: 5. Set up the integral to find the volume of the solid whose horizontal base is a circle of radius 2…

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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: Set up a sum of definite integral(s) that is equal to the volume of the solid whose base is R and…

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Q: 1. Find the volume generated by revolving the area bounded by the curve y = (1 – x²)² and the x–…

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Q: Find the volume of the solid that results when the region enclosed by y= x² and y = 12 - x is…

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

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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: Compute the volume generated by the curve = 4 y = z about x-axis between x = 2 and x x2

A: Given curve is  revolved around x-axis ,so now we will find volume generated by intigration between…

Q: If we want to find the area between the curves x = −y 2 + 1 and x = y 2 − 1, shall we integrate with…

A: Given curves are x=-y2+1 and x=y2-1

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 a right circular cone with height 18 and base radius 9 using integration.

A: Take a cross-section area of thickness dx at a distance x from top, integrate it from 0 to 18.

Q: Find the volume of the area bounded by the line y = 3x + 4 and the curve y = x² if it is revolved…

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Q: 4. Compute the volume rotating the area shown through one revolution about the x-axis. generated by

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Q: generated

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

Q: ut the line x = 3.

A: The parabola equation is given , x2 = 4y. The equation of line is given , x = 4 - 2y. The volume…

Q: Use a double integral to find the volume of the indicated soli 40 z 30 z = 25 – xy 20

A: Given: z=25-xy y=x    and   y=5

Q: What is the volume in the first octant bounded by x2 = 16 – y and z + y = 16.

A: Given curves are

Q: 3. Find the volume of a sphere with radius r by integration.

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Q: 2) Find the volume generated by the area bounded by y = x², y = 4x, revolved about x-axis.

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Q: om

A: Computing the volume generated by rotating the area through one revolution about the x-axis.…

Q: The area bounded by the curve y^2 = 12x and the line x = 3 is revolved about the line x =3. What is…

A: Recall: Formula for volume,    V=π∫ab(radius)2dy Given,  y2=12x Substitute x=3 in the above…

Q: Write the Integral(s) for the VOLUME generated by revolving the region bounded by: y = x?, y = 12 –-…

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

Q: 6. What is the volume generated when the area in the first quadrant bounded by the curve x2 = 8y,…

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Q: Find the volume of a solid extending from y = 2 to y = 5 if every cross section has area A(y) = 5.

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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: 2 Eualuate the inteyral 22 -- taken. throughout the volume • f sphere

A:

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 obtained by rotating the area bounded by y=x^4 and y=1 around the line y=8

A: Graph y = x4, y = 1 and y = 8 to find the boundary points as follows.

Q: What is the volume generated when the area bounded by y=2x2+1; x=1; x=2 is revolved about the line…

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Q: Find the volume generated by revolving the region bounded by y= 3Sqrt(x-1)and y=x-1 about y=-1

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Q: Determine the volume generated when the area bounded by the curves y-sinx and y%3cosx from x-0 to…

A: Aim: We need to find the volume of the solid obtained by revolving the bounded region (light yellow)…

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 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: Determine the volume generated when the area bounded by the curves y-sinx and y=cosx from x=0 to…

A: Solution :-

Q: 1. Show by integration that the volume V of a right circular cylinder with base radius r and height…

A: We’ll answer the first part of this question. since due to complexity. Please submit the question…

Q: Find the volume generated by revolving about the x – axis the area bounded by y^2=4x and x^2=4y

A: The volume generated by revolving the area bounded by the curves fx and gx is V=∫abπfx2−gx2dx. The…

Q: Find the volume generated by revolving about the line x - 4 = 0 the area bounded by the curve x2 =…

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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: Solids of Revolution ( refer to the image )

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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 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…

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.