Find the Volume generated by revolving the area bounded by the given curves and lines revolved about the given axis of rotation. y = x²/(x+2)       and y = x² - x revolved about the y-axis Please show complete solution.

Q: Find the volume of solid generated by revolving the area bounded by y³=x, y=2 and x=0 about the…

A:

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

A:

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: Find the volume of the solid bounded by y = x² +1 and the line y = -x + 3, revolved about the line y…

A: Given curve y = x2 and line y = -x +3

Q: y = 9x² and y = 0 about x = -4

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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

A: The given problem is to find the volume generated by revolving the region bounded by given curves…

Q: Find the volume of solid generated by revolving te area enclosed by : x=y²+1, x=0,y=0 and y=2 about:

A:

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

A:

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

A: As per rule of Barbtleby we can solve only one question at a time and we can solve only three…

Q: Compute the volume of the solid obtained by revolving the graph of y =1+x^2/2 on [0,1] about the…

A:

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

A:

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

A:

Q: Find the volume of the solid of revolution formed by rotating the area under y=9-x2 over [0, 3]…

A: Given curve is y=9-x2 ,[0,3]

Q: Find the volume of the solid generated when the area bounded by the curve y = Vx, the y-axis, and…

A:

Q: Evaluate the volume of the surface of the shaped recreated by revolving the line y = 1/x as x goes…

A: Solution is written in below steps.

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

A:

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: Find the volume generated by revolving the area enclosed by the curve x^2 + y^2 = 25 about the line…

A: We will find out volume of solid of revolution.

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

A: The equation of the curves are  C1: y = x2C2: x= 2C3: y = 0 The axis of the revolution is x = 2 To…

Q: Find the volume of the solid of revolution  obtained by revolving the region bounded by y=x-x2 and…

A:

Q: Find the volume of the solid formed by revolving the region bounded by y=6x−x2,y=0 about the x-axis

A:

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

A:

Q: Determine the volume of the solid that will be generated by revolving the area bounded by the given…

A:

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

A:

Q: FIND THE VOLUME GENERATED ABOUT THE BY REVOLVING THE AREA ENCLOSEP BY THE CURVE x+y%= 16 9-AXIS.

A: Here we have to find the volume bounded by the area about y-axis

Q: Find the volume of the solid generated when the region enclosed by y = root(x+3), y = root(3x+1),…

A:

Q: Find the volume generated by revolving about the line x=0 the area bounded by the curve y^(1/2) =…

A:

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

A:

Q: Find the volume of the solid generated by revolving the region bounded by the y = x2 and y=6x-2x2…

A: Given that y = x2 and y = 6x- 2x2 and we find volume about the y-axis and plot the graph. Here i…

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,…

A:

Q: Find the volume of the solid formed by revolving the region bounded by           y = x − x3 and the…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the curves y = 2x2 and y =…

A:

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)…

Q: : Find the volume of the solid generated by revolving the shaded region about the x-axis: y = sinx…

A:

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: Find the volume of the solid of revolution generated by revolving y = 9-x from x= - 3 to x= 3 about…

A: Given f(x)= 9-x2    where -3≤x≤3 To find the volume of the solid of revolution here use The Disc…

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

A:

Q: Find the volume of the Solid generated by revolving the region bounded by x = (1- y). x= 2,/y and…

A:

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

A:

Q: Find the volume of solid generated by revolving the area bounded by y = 8x and y = 2x about y=4.

A:

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 generated by revolving the area bounded by y = x^2 - 2x + 3 and y = 3 about the line…

A:

Q: Find the volume of the solid generated by revolving the shaded region about the y-axis. y 3

A:

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

A:

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.