) Find the volume formed by rotating the region enclosed by: x = 3y and y = x with y > 0 about the y-axis

Q: Find the volume of the solid generated by revolving the region enclosed by the triangle with…

A: If  you like the solution then please give it a thumbs up.. The Answer is:     Volume = 4π3

Q: Find the volume of the solid generated when the plane region bounded by x = y? and x + y = 2 is…

A: To find the volume of the solid generated when the plane region bounded by  x=y2 and x+y=2 is…

Q: Find the volume generated by revolving the area bounded by x? + 4x + 4y + 8 = 0 and y = -2 about the…

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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: Find the volume generated by rotating the given region about the specified line. R, about AB

A: On revolving the region R1 around the line Ab, the resulting solid obtained will be a cone.   This…

Q: Find the volume of the solid generated by revolving the given plane area having the given boundaries…

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Q: 3. Use cylindrical shells to find the volume of the solid eenerated when the shaded region is…

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Q: FIND THE VOLUME GENERATED BY REVOLVING THE AREA BOUNDED BY THE GIVEN CURVES AND LINES

A: Given curves equation is x2-y2=9 ⇒ x2=y2+9 ⇒ x=y2+9   ⇒ fy=y2+9  and line equation is  y=2x-6    ⇒…

Q: Find the volume of generated by rotating the region bounded by x = 4y – y? and x = 0 (a) about the…

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Q: use shell methed to the volume by rotating the region under y=x 0ver [1,4] about X= -3.

A:

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = x2 + 1, y =…

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Q: Find the volume generated by rotating the given region about the spcified line. R about y=0

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Q: Sketch the region R bounded by the graphs of x = (y – 1)² and x = 9. Use cylindrical shells to…

A: Given the region R bounded by the graphs of x=(y-1)2 and x=9. We have to use cylindrical shells to…

Q: Sketch the region bounded by the curves: y = e*,y = Inx, x = 1 and x = 2, then find, the area of…

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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 generated by rotate the region R about x = -1, when the R bounded by y = 0.5x, y = 8…

A: Use the disk method :

Q: A region bounded byf (y) = Vỹ + 1, y = 4, y = 9, and x = 1 is shown. What is the volume of the solid…

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Q: Sketch the region R bounded by the graphs of x = (y – 1)² and x = 9 Use cylindrical shells to…

A: The given region bounded by the graphs: x=(y-1)2 and x=9 The graph of the above region: To find the…

Q: Find the volume generated by rotating the region bounded by y = x, x = 1, and y? = 4x, about the…

A: Given curves are y=x, x=1   and  y2=4x We have to calculate the volume generated by these curves…

Q: Find the volume generated by revolving the area 1 bounded by y = 2, x = 5, and y = 0 about the…

A: Given that to find the volume generated by revolving the area bounded by  y=1x3+17x2+72x,  x=2,…

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

A:

Q: Find the volume generated by rotating the area bounded by y = ,* = 2, x = 7, and y = 0 about the y…

A: The solid obtained by rotating the region between the grah of fx and the x-axis from x=a to x=b…

Q: 1) Find the volume formed by rotating the region enclosed by: x = 3y and y³ = x with y ≥ 0 about the…

A: answer is in next step . please give a like!!!

Q: Find the volume generated by revolving the region enclosed by x -y and y=x+2 about у-аxis.

A: We have to find the volume.

Q: Find the volume generated by revolving the area bounded by xy=4, x=1, x=4 and the x-axis about the…

A:

Q: Find the volume of the solid generated by revolving the given plane area having the given boundaries…

A: The given plane area with boundaries is y=x2,  y=0,  x=5. The main objective is to find the volume…

Q: b) Find the volume generated by revolving the region enclosed between y = -2x, x = -3, and x – axis…

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Q: B. Find the volume generated by revolving the region enclosed by x - -y and y=x+2 about У-аxis. 20%

A:

Q: Find the volume formed by rotating the region enclosed by: 5y and y = x with y > 0 about the y-axis…

A: Given Data The first equation is x=5y. The second equation is y3=x.   Equate the given both…

Q: Find the volume generated by rotating the given region about the specified line. R, about BC

A: In this question, we find the volume by rotating the region R1 about the line BC.

Q: Determine the volume obtained by rotating the area enclosed by y = x(4 – x) and y 0 about the line x…

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Q: 1. Use cylindrical shells to find the volume of the solid generated when the shaded region is…

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

Q: y y = x2 + 2 A В 1 2

A: The volume obtained by rotating region between two curves f(x) and g(x) around y=k over the interval…

Q: Find the volume of the solid Formed by revolving the region bounded by the graphs OF y=x +1, y = 0,…

A: Find your answer below

Q: Find the volume generated by rotating the region bounded by y = x, x = 1, and y? = 4x, about the…

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Q: The region bounded by f(x) = - 3x? + 15x + 42, x = 0, and y O is rotated about the y-axis. Find the…

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Q: (4) Find the volume of the solid obtained by rotating the region bounded by y = r, y = 0, x = about…

A: Given:- y=x3,  y =0 and x=1 To find:- Volume of solid about line x=2

Q: Find the volume generated by revolving the area 1 bounded by y -, x = 3, x = 9, and y O about the…

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Q: A. Find the volume generated by revolving the region enclosed by y = 4Vx, y = %3D 2-x and y =x +3…

A:

Q: = 3, Find the volume of the solid obtained by rotating the region bounded by y = x , y = 0, and a =…

A: In this question we have to just find the volume generated by rotation.

Q: . Find the volume bounded by z = 9 –x² – y² and z = 0. Give a numerical %3D answer.

A: Given that the region is bounded by z=9-x2-y2 and z=0. We know that the volume bounded between…

Q: Find the volume of the solid obtained by rotating the region bounded by y = 6x?, x = 1, and y = 0,…

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Q: 1. Find the volume of the solid generated by revolving the region bounded by the parabola x =y? and…

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Q: 5. Use cylindrical shells to find the volume of the solid generated when the region enclos between x…

A: The formula for the volume of the solid generated by a curve using the shell method is given by…

Q: Find the volume formed by rotating about the y-axis the region enclosed by: x = 11y and y = x with y…

A:

Q: Find the volume of the solid generated by revolving the region bounded by y = 3vx, y = 6, and x = he…

A: Given,         y=3x, y=6, and x=0,  about x-axis.

Q: 9. Find the volume generated by revolving the given plane area about the given line using the disc…

A: We are given two regions: (a) y=2x2, y=0, x=0, x=5 about x-axis. (b) x2-y2=16, y=0, x=8 about…

Q: Find the volume formed by rotating about the y-axis the region enclosed by: 8y and y* = x with y > 0

A: Here diagram for given problem is:

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.