Find the volume generated by revolving the area enclosed by the curve x^2 + y^2 = 25 about the line y – 8 = 0.

Q: Find the volume of the solid Formed by revolving the bounded by the graphs oF fox) =v9-X, y-axis %3D…

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Q: The curve represented by y = x² from (0, 0) to (1, 1) is rotated about the x-axis, what is the…

A: Graph of given problem:

Q: Apply integration technique to find the volume generated by revolving the area bounded by the…

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Q: Draw the area bounded by function y = x^2 + 1 and line y = 5, then calculate the volume of the solid…

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Q: Find the volume generated by revolving the region bounded by y=−x^4+3x^3, y=0  revolving about the x…

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Q: Find the volume generated by revolving the area bounded the lines x+y=6, x=0 and y=0, about x-axis.

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Q: Find the volume formed by revolving about the line y = 2a, the area bounded by that line, the curve…

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Q: Find the volume of a cone generated by revolving about the y-axis the area bounded by the line…

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Q: Find the volume formed by rotating the region above the curve y=x^3 and under line y= 1 about…

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Q: Find the volume generated by revolving the region above the curve y=x3 , under the line y=1, and…

A: Given: y=x3, y=1, x=0 & x=1 From the given curve the bounded region is as shown below: Apply…

Q: Determine the volume of the solid formed by revolving the area bounded by y= x- 2x and y=0 about the…

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x)and the x−axis…

Q: find the volume of the solid generated by revolving the region bounded by y =sqrt x, y =x-2 in the…

A: According to the given information, it is required to find the volume of the solid generated by…

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: As per the guidelines i am solving first question. 1. Consider the given curves, y=x2, x=3 and y=0.…

Q: Find the volume formed by revolving about the line y = 2a, the area %3D bounded by that line, the…

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: y2=2x+4 and y2=4-2x, about y-axis The intersection point of the curves is calculated below,…

Q: Find the volume generated by revolving the region above the curve y=x3 , under the line y=1, and…

A: Figure of y=x3 , y=1 and x=1

Q: Determine the volume of the solid formed by revolving the area bounded by X+y-6 = 0, y=3 and x=0…

A: The solid formed by revolving the area bounded by x+y-6=0, y=3 and x=0 about the y-axis.

Q: y = 9x² and y = 0 about x = −4

A: Given:        y=9-x2 and y=0         x2=9           x=3 about x=-4

Q: ) Find the volume of the solid formed by revolving the region bounded by the cu y = √9-x² and y = 0…

A: To Find:  Volume of the solid formed by revolving the region bounded by the curve       y = 9 - x2 ,…

Q: Find the volume of the solid generated from revovling the area of the region bounded by the curve y…

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Q: Find the volume generated by revolving the area bounded by y = x3 – x2 , x-axis, about y-axis by…

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Q: Find the volume of solid generated by revolving the area bounded by y = 8x and y = 2x about the…

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Q: Find the volume if an arch of y=sin⁡2x (bounded by the x-axis) is revolved about the x-axis

A: Volume of revolving  of y = f(x) about X-axis  Vol =∫abπ(f(x))2dx

Q: What is the volume obtained by revolving the are biunded between the lines y=x, y=2x and x=4   about…

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Q: Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 25 about the line y…

A: Explained below

Q: Find the volume of the solid generated by revolving the region bounded by y =4(sqrt(sin x))​, y = 0,…

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Q: Find the volume of the solid generated when the area bounded by the curve y = square root of x,…

A: Find the volume of the solid generated when the area bounded by the curve y=x, y-axis and the line…

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Q: Find the volume of the cone generated by revolving about the y-axis the area bounded by the line 2x…

A: Your problem was not so clear. There are two different functions, the graph is not matching with the…

Q: Determine the volume of the solid formed by revolving the area bounded by y= X² and x=y² about the…

A: The formula for the volume of the solid formed by revolving the region bounded by the curves, y=f(x)…

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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: 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 about the line 0x the area bounded by the curve 1 (포2 - 1)…

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Q: Find the volume of the solid obtained by revolving the region bounded by the curve y=1 / (1−sinx)…

A: We have given a region bounded by the curve y=11-sinx, 0≤x≤π3the region is show in the graph-

Q: The area bounded by the line x=1 and the curve y^2-x=3 is revolved about the line y=4. Using Shell…

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Q: Find the volume of the cone generated by revolving about the y-axis the area bounded by the line 2x…

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Q: Find the volume of the solid generated by revolving the area bounded by y = Inx; y = 0 and x = 4…

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Q: Find the volume of a solid obtained by revolving the curve x2=y-3 about x-axis from x=1 to x=3

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Q: Find the volume of the cone generated by revolving about the y-axis the area bounded by the line 2x…

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Q: find the volume of solid generated when the regions enclosed between the curves y=x^2 and x=y^2 is…

A: Given curves, y=x2andx=y2 To find the volume of solid generated by these curves about x - axis.

Q: Find the volume of the region formed by revolving the region bounded by y=sqrt x, y=0, and x=4 about…

A: First, we sketch the region using a graphing calculator  The shaded region is rotating about the…

Q: Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 25 about the line y…

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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 of the solid generated by revolving the shaded region about the y-axis. y 3

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Q: Find the volume generated by revolving the area enclosed by the curve 4y² = 4x²-x+ about the y-axis.

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Q: Find the volume generated by revolving about the line x – 4 = 0 the area bounded by the curve x^2 =…

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Q: Find the volume generated by revolving the area enclosed by the curve 4y² = 4x²-x* about the y-axis.

A: Hint: First obtain the values of x for which y is zero to obtain the limits of the integration. Now,…

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.