use a theorem of Pappus to find the volume generated by revolving about the line x = 5 the triangular region bounded by the co-ordinate axes and the line 2x + y = 6

Q: The volume generated when the region bounded by y = x, y = 1, x = 0 is rotated about x axis is -

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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 of the solid generated by revolving the given plane area having the given boundaries…

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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 generate by rotating the given region about the specified line. R2 about BC

A: Integrating a small volume element within appropriate limits will result in the complete volume of…

Q: Find the volume generated by revolving the area 1 bounded by y 3, x = 4, and y = 0 about the y-axis…

A: Solution

Q: Y= x² x+2 and y=x²-x X revolved about the y-axis

A: Give curves y=x2x+2   and y=x2-x. The objective is to find volume generated by revolving the area…

Q: Find the volume obtained if the figure formed when the region bounded by y=x^2 and y = 2x is rotated…

A: NOTE: Refresh your page if you can't see any equations. . here have to find the intersection…

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

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Q: Find the volume generated by revolving the area 1 bounded by y -, x = 2, x = 4, and y = 0 about the…

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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: 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 generated by rotating the area bounded by 1 y = x = 2, x = 7, and y = 0 about the y…

A: To find the volume of the solid generated by rotating the area bounded by y=1x3+5x2+4x, x=2 , x=7…

Q: 1. Calculate the volume bounded by y = x², y = 0 and x = 2 rotated about the specified line, using…

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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: Find the volume generated by revolving the given bounded plane area about the line. Use shell…

A: Volume

Q: Find the volume in the first octant bounded by the cylinder x² +y = a² 2a and the lane z = x + v.

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Q: Use the Theorem of Pappus to find the volume of the solid that is generated when the region enclosed…

A: y = 8−x² given y = x²     given This means that 8- x² = x² 2x2=8 x=-2,+2 Then, y=4,4

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A: y=e-x2,y=0 & x=1 Using the method of cylindrical shells, volume generated- V=∫x1x22πxy2-y1dx

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

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Q: Find the volume generated by rotating the area bounded by each set of equations around the x-axis.…

A: The volume for solid of revolution for a curve is the volume of object determined by a curve fx…

Q: Use the Theorem of Pappus to find the volume of the solid of revolution The torus formed by…

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Q: Use the Theorem of Pappus to find the volume of the solid of revolution. the torus formed by…

A: We have to use theorem of pappus to find the volume of solid of revolution The torus formed by…

Q: The area enclosed by y = 4x - x^2 and 2y = 2x + x^2 is revolved about the line x = -1. Using a…

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Q: Find the volume generated by revolving the area bounded by y² - 4y - 4x + 4 = 0 and x = 1 about the…

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Q: Determine the volume generated by revolving the region bounded by the lines y = 4 - x, x = 0, and y…

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Q: Use the Theorem of Pappus to find the volume of the solid of revolution The solid formed by…

A: Theorem of Pappus: The volume of solid of revolution generated by revolving a lamina about an axis…

Q: The region in the first quadrant bounded by x2 + y² = 1, x 2, and y = 1 is revolved about: 1- The…

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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: Find the volume generated when area bounded by axes and line 3x + 2y = 12 is revolved about y-axis…

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Q: Use the method of disks to find the volume generated when the region bounded by x = y° and x = 4 is…

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Q: Find the volume generated by revolving the region bounded by y= 3Sqrt(x-1)and y=x-1 about y=-1

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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: The region bounded by y = x', y = 0, and x = 2 is revolved about the line x= 2. Find the volume of…

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Q: Find the volume obtained by rotating the region bounded by the curves x = y² and y = x³ about the…

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Q: Find the Volume generated by revolving the area bounded by the given curves and lines revolved about…

A: Solution is given below:

Q: Consider the 2D region bounded by y = x, y = 0 and x = 1. Use shells to find the volume generated by…

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Q: Find the volume obtained by rotating the region bounded by x = y² and ¤ = y around the r-axis. %3D

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Q: A torus is formed by revolving the region bounded by the circle x2 + y2 = r2 about the line x = R,…

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Q: Use the Theorem of Pappus to find the exact volume of a general cone created by rotating a triangle…

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Q: find the volume of the region in the first octane bounded by the coordinant planes, the plane y + z…

A: See the details solution in below

Q: Find the volume generated by revolving the area bounded by : 2, x = 5, and Ж — x3 + 9x² + 18x y = 0…

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Q: y = x^5 1- y = x y 0.5 0.5

A: Recall: Formula for volume    V=π∫abouter radius2-inner radius 2dx We have a=0, b=1, outer…

Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y = -2 about the…

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Q: Find the exact volume generated by revolving the region bounded by f(x) = 2x^2 + 10 and g(x) = 4x +…

A: The volume generated by revolving the region by line y= 10 The given functions are fx=2x2+10 and…

Q: Use the disk method to find the volume when the region bounded by y = ex + 1, x = 0, x = 1, and y =…

A: y=ex+1,  x=0,  x=1  &  y=0.

Q: Find the volume obtained by rotating the region bounded by x = y^2 and x = y around the x-axis.

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Q: Consider the 2D region bounded by y = x5/2, y = 0 and x = 4. Use disks or washers to find the volume…

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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.