Find the volume of the solid that is created by rotating the area enclosed by y = Vx + 3, y = 3, and x = 4 rotated around the x-axis.

Q: Find the volume of the solid that results when the area of the region enclosed by y= Vx+1, x = 4,…

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Q: Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by…

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Q: Find the volume of the solid whose base is the region enclosed by y = x² and y 3, and the cross…

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Q: Find the volume of the solid of revolution bounded by y = 1/(x+1), x = 0, x = 2, and the x-axis, and…

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Q: Find the volume of the solid that results when the region enclosed by x = - y² + 7, and x = y + 4 is…

A: We first find the y values of the intersecting points by setting the equations…

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 generated when the region enclosed by y = sqrt(x), y = 0, and x = 49 is…

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Q: Find the volume of the solid. y=x2, x=0; x=2, y=0, about the x-axis

A: use the volume of solid of revolution formula,

Q: Find the volume of the solid formed by rotating the region enclosed by y=x3and y=4x in the first…

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Q: Find the volume of the solid formed by rotating the region enclosed by eA# + 5, y = 0, x = 0, x =…

A: olume by shell method is given below

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

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Q: Find the volume of the solid obtained by rotating the given curves about the specified axis.

A: Introduction: The formula of washer method to find the volume of the solid is given by,…

Q: Find the volume of the solid generated by revolving the area of a circle. (x-3)²+y²=9; about the…

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Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y = x°, y =…

A: We have to determine volumes of solid

Q: Find the volume of the solid generated by rotating the area bounded by the lines y=x, y=2x and x=3…

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Q: Find the volume of the solid generated when the region enclosed by y x, y 6- x, and y = 0 is…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 8x, x = 1, and y = 0,…

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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: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

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Q: Find the volume of the solid that results when the region enclosed by 4x 0, x = 1, and y = 0 is…

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Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y = 0, y = 6+x6…

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Q: Determine the volume of the solid of revolution which is formed when the area bounded by x = -4.5, x…

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Q: Find the volume of the solid generated when the region enclosed by y = Vx + 2, Y = /5x, and y = 0 is…

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Q: Find the volume of the solid generated by revolving 67 from y = 1 to y= 2 about the y-axis.

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Q: Find an expression for the volume of the solid of revolution obtained by rotating the region in the…

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Q: What is the volume of the solid generated when the region surrounded by y = vx, y = 2 and y = 0 is…

A: Given: y=x,  y=2  and  y=0Rotation around y−axis

Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y = 0, y = 7+…

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Q: Find the volume of the solid obtained by rotating the regic y = e-*, y = 1- e-*, and x = 0 about the…

A: Given: To find the volume of the solid obtained by rotating the region bounded by the curves

Q: Find the volume of the solid generated by revolving about the y-axis, the area bounded by y = x^2 ,…

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Q: Find the volume of the solid generated when the region enclosed by y=sqrt(x+4), y=2x and y=0 is…

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Q: Find the volume of the solid that results when the region enclosed by y = Vx, y = 0, and x = 81 is…

A: We have to find the volume of region.

Q: Find the volume of the solid generated by rotating the area bounded by the y=sqrt(x-1) and y=(x-1)^2…

A: Given:y=(x-1)    and    y=(x-1)2 To find out: The volume generated by rotating the area bounded by…

Q: Find the volume of the solid that is obtained by revolving the region about the indicated ax About…

A: Explanation and solutions is given below....

Q: Find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=4+x3 about…

A: Solve

Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

A: Here, we need to find the volume of the solid generated by revolving the shaded region about the y -…

Q: Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y =…

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Q: Find the volume of the solid generated by revolving the shaded region about the given axis.

A: We need to find volume.

Q: Find the volume of the solid generated when the region enclosed by y = sqrt(x+1), y = sqrt(5x), and…

A: The volume of the region bounded by the curves y1(x) and y2(x) is given by the formula…

Q: Find the volume of the solid whose base is the region bonded by y=x^2 and y= 1-x^2 and whose cross…

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Q: . Find the volume of the solid generated by revolving the shaded region about y-axis. ty 2. X+2y-2

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Q: Find the volume of the solid obtained by revolving the area enclosed by y = 2x, y = 2 and r = 0…

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Q: What is the volume of the solid of revolution generated by rotating the area bounded by y%3D2, y3 3,…

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Q: Find the volume of the solid that results when the region enclosed by Y = Va + 1, y = 1 and a = 1 is…

A: Here we have to find the volume of the solid that results when the region enclosed by y = √x + 1,…

Q: Find the volume of the solid formed f(x) Vx, y = 0, X = %3D about the x-axis.

A: Here we have to find the Volume of the solid formed by revolving  the region bounded by,  f(x)=√(x),…

Q: Find the volume of the solid that is created by rotating the area enclosed by y = Va + 3, y 3, and z…

A: Concept Used: Washer method The volume of the solid generated by rotating the area around the x axis…

Q: Find the volume of the solid formed by rotating the region bounded by y = x² + 3, x = 0, x = 2, and…

A: The solid is formed by rotating the region y=x2+3, x=0, x=2 and y=0about the x-axis

Q: Find the volume of the solid whose base is the semicircle y = v9 – x2 where -3 < x < 3, and the…

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Q: Find the volume of the solid generated when the region enclosed by y = √ x + 1, y = √ 2x,and y = 0…

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Q: Find the volume of the solid generated by revolving the shaded egion about the y-axis. x- 4 tan y 4

A: Topic:- application of integration

Q: Find the volume of the solid of revolution generated when the area bounded by the curve y = Vx, y=0,…

A: As per as our I am supposed to answer only one from these two different question . So I will answer…

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.