Find the volume of the Solid generated by revolving the region bounded by y = -2x² and y = x² – 3 , in the 4th quadrant about the: 1) y-axis 2) x-axis

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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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 obtained by rotating the region in the first quadrant bounded by the…

A: We have to find the volume of the solid by rotating the region in the firs qudrant bounded by the…

Q: Find the volumes oF the solids geverated by revolving +he regions bounded by the graphs oF the…

A: Given:-  the region bounded by  y=2x2y=0  and x=2rotating about the x-axisusing washer/disk method…

Q: Find the volume of the solid generated by revolving the region enclosed by y = 4x , y= 0 rotated…

A: It is a method for calculating the volume of a solid of revolution of a solid-state material when…

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 of the solid generated by revolving the region bounded by y=6x−x^2 and y=0 about the…

A: Given : region is bounded by y=6x-x2 and y=0 To find : volume of the solid generated by revolving…

Q: Find the volume of the solid formed by revolving the region bounded by y = (x – 2)2 and y = x about…

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Q: Find the volume of the solid formed by rotating the region enclosed by 4x y = e about the x-axis. +…

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Q: Find the volume of the solid generated by the revolving the region enclosed by y=(x+1)2, y=-x+5 and…

A: Given y=x+12 , y=-x+5Intersection pointx+12=-x+5⇒x2+2x+1=-x+5⇒x2+3x-4=0⇒x2+4x-x-4=0⇒x+4x-1=0∴ x=1…

Q: Find the volume of the Solid generated by revolving the region bounded by y = vx and the lines y = 1…

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Q: Find the volume of the solid generated by revolving the region bound by y = x and about the y-axis.

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Q: A. Determine the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 54x – 6x and y = 0 about…

A: Given:y=54x-6x2  and y=0Vx=∫ab 2πx fx dx

Q: Find the volume of the solid obtained by rotating the region bounded by y=7x^2, x=1, and y=0,…

A: Given:-     y=7x2                   x=1                   y=0         about x‐axis. ∴volume v=∫ab…

Q: Find the volume of the solid of revolution formed by rotating each bounded region about the x-axis.…

A: Given:        f(x) = 1 - x ; x = 0 , y = 0    To find the volume of the solid of revolution…

Q: Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by…

A: Solution: Consider the given equations are y = x + 1 y = 0 x = 1 and  x = 4 If we construct bounded…

Q: What is the volume of the solid generated by revolving about the x-axis, the region bounded by y =…

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Q: Find the volume of solid generated by revolving the region bounded by the lines y = 0, x = 2 and…

A: We have to find the volume of solid bounded by given region revolving around X-axis.

Q: Find the volume of the solid generated by revolving the region bo x-axis. 16) y = √ , y=0, x= 1, x =…

A: Introduction: To determine the volume of specific solids, one can utilize the disc method, an…

Q: Find the volume of the solid generated by revolving the region bounded by y=sqrt x, y=-1/2x+4, x=0,…

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Q: Find the volume of the solid generated by revolving the region bounded by the line y = 0 and curve y…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 3x², x = 2, x = 5 and y…

A: Topic- application of integration

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: Find the volume of the solid generated by revolving this region about the y -axis y = x, y = 2x, x =…

A: First draw the graph of all curves than use integration to find volume of the solid formed.

Q: Find the volume of the solid generated by revolving the region bounded by y = x² + 1, y = x + 3…

A: Given that,  y = x2 + 1y = x + 3 The Axis of rotation = X-axis In the Disk/Washer method strip is…

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

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Q: Find the volume of the solid generated by revolving the region bounded by y = x2 +1, y = x+ 3 about…

A: The volume of the solid of revolution  about x-axis is obtained as Volume=∫abA(x)dx Where…

Q: Find the volume of the solid obtained by rotating the region bounded by y = 7x², x = = 1, and y = 0,…

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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

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

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Q: Find the volume of the solid obtained by revolving the region bounded by y = x², y = (x – 6)², and…

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Q: Find the volume of the Solid generated by revolving the region bounded by y = Vx and the lines y = 1…

A: Consider the graph:

Q: 5. y = 4x – x², x = 0 , y = 4 , revolved at y axis -

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Q: Find the volume of the solid generated by revolving around the y- axis, the region bounded by 1 y =…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 9x2, x = 4, x = 5, and y…

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Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y arctan(r), x…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 4x², x = 1, and y = 0,…

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Q: Find the volume of the solid generated by revolving the region created by the curves, y* _y² y² 2…

A: The given curves can be plotted by:

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

A: Topic = Application of integration

Q: 2. x = 4y – y² and x = 4 – y -

A: follow next step

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: Find the volume of the solid generated by revolving the region bounded by y = 2x – a2 and y= x

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Q: Find the volume of the solid generated by revolving the region enclosed by y=x3, y=8 and x=0 about…

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Q: By Sketching the graph, find the volume of the solid generated by revolving the region given by, y =…

A: If is a function, then the independent variable x is called the input of the function and the…

Q: Find the volume of the solid generated by revolving the regionbounded by y = √x and the lines y = 2…

A: The curve given is  y = √x and the lines y = 2 and x = 0 about the line y = 2. The graph of the…

Q: Find the volume of the solid generated by revolving the region bounded by y = 3x – x² and y x2 about…

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Q: Find the volume of the solid generated by revolving the region bounded by y = x³,y = 0, x = 2 about…

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Q: Find the volume of the solid generated by revolving the regionbounded by y = √x and the lines y = 2…

A: To find the volume of the solid generated by revolving the region bounded by  y=x and the lines y=2…

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.