Find the volume of the solid formed by rotating the region between the y=sqrt(x)curve  y=2 line and the x=10 line around the y=2 line.

Q: Find the volume of the solid obtained by revolving the curve x²=y-3 about x-axis from x=1 to x=3

A: The volume generated by revolving any curve y=f(x) about x-axis  from x=x1 to x=x2 is given by V=…

Q: Find the volume of the solid formed by revolving the area bounded by the parabola y2 = 9x and the…

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Q: Find the volume of the solid generated by revolving the region between the parabola x = y² +1 and…

A: Given Data: Curve 1: x=y2+1 ......(1) Curve 2: x=5 ......(2) The graph of the region enclosed by the…

Q: Find the volume of the solid obtained by revolving about the x-axis the region between y = 2x and…

A: Given curves:- y=2x and y=x2

Q: Determine the volume of the solid formed by revolving the area bounded by y² = 4x and x²= 4y about…

A: It is given that, y2=4x⇒y=2xand4y=x2⇒y=x24   Volume of solid formed by revolving the area bounded by…

Q: . Find the volume of the solid generated by revolving the area bounded by the curve y = In x, the…

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Q: Find the volume of the solid generated by revolving the curve y? – x8 – x2 = 60 between x = 0 - and…

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Q: Find the volume of the solid created by revolving the bounded region created by the graphs of y = Vx…

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

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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 formed by revolving the region bounded by y = x – a° and the x-axis (0…

A: The region bounded by x = f(y) and the y‐axis on [ a, b] is revolved about the y‐axis, then its…

Q: Find the volume of the solid obtained by rotating the curve y=x^2 , y= square root x , the lines x=0…

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

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Q: Find the volume of the solid generated by revolving the region between y = 4 – x2 and y = -x + 2…

A: The given regions are, y=4-x2 and y=-x+2 and the given line is, x=44-x=0 We can write the given…

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 formed by revolving the region bounded by the graph of the equation…

A: Volume of the solid formed by revolving the region bounded by the graph of the equation about the…

Q: Find the volume of the solid generated when the region between y = sinx and y = 0 for 0 ≤ x ≤ π is…

A: y=sinx  &  y=0  for  0≤x≤π

Q: The area enclosed between the two curves x² = 2y and y² = 2x is rotated about the x- axis. Determine…

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Q: Find the volume of the solid generated by revolving the region bounded by the curves y = 1- jx| and…

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

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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 of revolution  obtained by revolving the region bounded by y=x-x2 and…

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Q: Find the volume of the solid obtained by rotating the region bounded by the curve y = sin (7x) and…

A: Volume

Q: Find the volume of the solid formed by revolving the region bounded by the curves y = 3x²,x = 0, and…

A: Given : Curves y = 3x2, x = 0 and y = 3   To find : Volume of solid formed by revolving the region…

Q: Find the volume of the solid formed by rotating the area bounded by y = 1 the x- x+1 and y-axes, and…

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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 of the solid obtained by rotating this region about the line x = 3.

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Q: Find the volume of the solid obtained by rotating the region bounded by the curve y 3 - z and x-axis…

A: The volume for solid of revolution for the curve x2=3-y around x=0 on interval 0, 1:The volume for…

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

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Q: . Find the volume of the solid generated by revolving the region bounded by the y = -a2 + 6x – 8 and…

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Q: Find the volume of the solid generated by revolving the region bounded by the curves y=x and y=4x –…

A: TTt

Q: Find the volume of the solid generated by revolving the curve y=3vx between x = 0 & x = 3 about the…

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Q: Find the volume of the solid obtained by rotating the region bounded by the curve  y=sin(10x^2)…

A: The volume made by full revolution of area under y=f(x) about y axis between limits x=a and x=b is…

Q: Find the volume of the solid generated by revolving the region bounded by the y = 4x - x2 and y = 0…

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Q: Find the volume of the solid whose base is the region enclosed between the curve x = 1−y² and the…

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Q: Find the volume of the solid formed by rotating the region enclosed by 5x Y = e + 4, y 0, 0, = 0.9 ,…

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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 enclosed by the graphs of y =…

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

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

A: To find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

Q: Find the volume of the solid formed by rotating the region bounded by y = ² and y = x-axis using the…

A: Washer method

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 shaded region about the y-axis. y 3

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Q: Find the volume of the solid formed by rotating the region bounded by y = x² + 3, x = 0, x = 2, and…

A: The solid is formed by rotating the region y=x2+3, x=0, x=2 and y=0about the x-axis

Q: Calculate the volume of the solid obtained by rotating the region bounded by the parabola 4py = x²…

A: For the solution follow the next steps.

Q: Determine the volume of the solid of revolution when the region enclosed by the x  – axis, the curve…

A: Given, the region is bounded by the x-axis, the curve y=x12 and the line x=3,  Drawing the graph of…

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.