Q-3 calculate the Volume of the solid obtained by rotating the region bounded by the cerve y= 2X-X2 and the X-aXis about the y- axis 9= 2X- X2 and the X-axis about the y-axis

Q: a) Find the volume of the solid obtained by rotating the region bounded by the curves y = 2x + 1, x…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: Using disc method, volume is evaluated.

Q: The region bounded by y = x² – 3x + 2 and y = 0 is rotated about the y-axis. Find the volume of the…

A: The given curves are,

Q: 64. The area bounded by the curve y = 3 + 2x – x² and the line y = 3 is rotated completely about the…

A: Consider the given information: The area bounded by curves y=3+2x-x2 and the line y=3. To find the…

Q: The region bounded by f(x) = -2x2+16x+18, x-0, and y=0 is rotated about the y-axis. Find the volume…

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Q: The area cut off by the x-axis and the curve y = x2-3x is rotated about the x-axis. Find the volume…

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Q: The volume of the solid generated by revolving the region bounded by the graphs of the equations…

A: y=x2, y=0, x=2  about  y‐axisvolume=π ∫dc  x22-x21. dy     x=y  ,      x=2

Q: Find the volume of the solid generated by revolving the given region bounded by the line and curve…

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Q: Find the volume of solid generated when area bounded

A: Given: The area bounded by  y=x2 and y=x is revolve about x=2.

Q: Find the volume of the solid obtained by rotating the region bounded by the curves x2 −y2 =9 and x=5…

A: Consider the provided question, The graph of the given curve is drawn as, The required volume of…

Q: The volume for solid of revolution between the curves y = √49-x² and y=0 around the x-axis is (26/3)…

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Q: Find the volume of the solid generated by revolving the region bounded by the x-axis, the curve y =…

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

Q: 4. The region bounded by the curve y = x² + 1 and the line y = -x + 3 is revolved about the x-axis…

A: We have to find the volume of solid.

Q: Find the volume V of the solid generated by revolving about the x-axis the region under the curve y…

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Q: 3. Find the volume of the solid form by the region bounded by the curves y = =,y = 2-x is revolved…

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Q: Find the volume of the Solid generated by revolving the region bounded by y = -2x? and y = x2 - 3 ,…

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

Q: Find the volume of solid generated by revolving the region bounded by the curves and lines about the…

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Q: Geometry problems Use a table of integrals to solve the following problems.

A: Given Data The equation of the region is y=1x+4. The interval on x-axis is [0,12].   Arrange the…

Q: Find the volume of the resulting solid if the region under the curve y = 9/(x2 + 3x + 2) from x = 0…

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Q: alculate the volume of the solid obtained by rotating the region bounded by the function y = x^2,…

A: given function is y=x2the line y=-2 from x=0 to x=2find the volume V=∫abπfx2-gx2dx

Q: ermine the volume of the solid obtained by rotating the region bounded by y = √x and y = 3 and the…

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Q: The region bounded by the curve y = x², axis, and the line x = 2 is revolved about the y-axis. What…

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Q: The region between the curve y = - csc'x and the line y= - from x= 1 to x = /2 is revolved about the…

A: The given curves are: y=-csc-1x        and       y=-π2    from x=1  to  x=2

Q: b) [. obtained curve 1: Find the volume of the solid by rotating the region bounded by the y = -x² +…

A: Solve the following

Q: Find the volume of the solid generated by revolving the region bounded by the x-axis, the curve y =…

A: Hi, thank you for the question. There are multiple question in the request. And the solution of each…

Q: ind the volume of the 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 solid obtained when the region enclosed by the curve x= 2 − y^2 and the line…

A: Given curve x=2-y2 and x=y revolved about line x=-2

Q: Find the volume of the solid obtained by revolving the curve y=xe^-x 0<=x<infinity along x axis

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Q: 1. Find the area of the region bounded from the right by the curve x = 4 – y? , from the left by the…

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Q: Find the volume of the solid generated by revolving the region about the y-axis. 3π 4 ‚ x = 0, y = -…

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Q: A solid of revolution is formed by revolving the region bounded by the graph of f(x) = 4e¬2x, the…

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Q: 1. Find the area of the region bounded from the right by the curve x = 4- y2, from the left by the…

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Q: The volume of the solid generated by revolving the region bounded by the graphs of the equations…

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Q: Determine the volume of the solid generated by revolving the region between curves about the line x…

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Q: 2. The region in the first quadrant bounded by the graph of y= 4- xand the coordinate axes, is…

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Q: The region bounded by x2 + (y – 1)² = 1 is rotated about the y-axis. Find the volume of the…

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Q: 1. y = 3x - x² and y = 3-x Find the volume of the solid generated by revolving about the line x = 4…

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Q: 2. Find the volume of the solid obtained by rotating the region bounded by the curves y = x² and x =…

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Q: 2. Find the volume of the solid generated by revolving the region bounded by the parabola y = x…

A: I use washer method

Q: 9. Determine the volume of the solid obtained by rotating the region bounded by y = x - 6x+9 and y…

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Q: The region bounded by y = x – 3x +2 and y = 0 is rotated about the y-axis. Find the volume of the…

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Q: The region in the first quadrant bounded by the graph of y sec x, x=, and the axes is rotated 4…

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Q: The region between the curve y = 1/x2 and the x-axis from x = 1/2 to x = 2 is revolved about the…

A: Graph the given situation, shaded region is being rotated about y axis

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of y = x3 , x =…

A: Here, the given region is bounded by the graphs of y=x3, x=2 &amp; y=0 is shown:

Q: 4. Find the volume of the solid generated by revolving abou the y-axis the region in x = 4y – y' and…

A: To fins the volume of the solid generated revolving around y axis

Q: The region in the first quadrant bounded by Y = -3x + 6, the x-axis and the Y-axis is rotated around…

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Q: 4. Calculate the volume of the solid of revolution obtained by revolving the region bounded by the…

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Q: Compute the volume of the solid formed by rotating the region pounded by = 1 - x² and y = 0 about…

A: Given:- y = 1-x2 and y=0 To find:- Volume about x axis of solid formed by given curves and line

Q: 5/ Find the volume of the solid generated by revolving the area enclosed by y= x², y-0, x-1 about 1)…

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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.