Find the volume of the solid generated by revolving the region bounded by the curves x 12(y² - y) and x = 0 about the x- %3D axis.

Q: Find the volume of the solid that results when the region enclosed by y = e2", y = 0, x = 0, x = ln…

A: Topic:- application of integration

Q: Find the volume of the solid obtained by rotating about the x- axis oF the region bounded by y= x ,…

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Q: Find the volume of the solid formed by rotating the region bounded by the curve y = v3 and the line…

A: Follow the procedure given below.

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 obtained by rotating the region bounded by y = (x-1)(x-3)²and the…

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Q: Find the volume of the solid obtained by revolving the region bounded by the graph of f(x) = 8e-lx,…

A: Given the curves: fx=8e-7x, x axis, y axis, x =6rotated about y axis

Q: Find the volume of the solid obtained by revolving the region between the graphs of y = x² and 3x…

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Q: Find the volume of the solid that results when the region enclosed by y = e2", y = 0, x = 0, x = ln…

A:

Q: Find the volume of the solid obtained by rotating about the x-axis, the region under the curve. y =…

A: Consider the curves, y=2x+3,y=0,  x=0    to  x=3 Consider the region:

Q: xy = 4, y = x,y = 1; about the x-axis.

A: Find your answer below

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

A:

Q: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x-3y-2= 0 is…

A: We know that if y=f(x) ,and y=g(x) are two curve intersecting at  x=a and x=b  the required volume…

Q: Q6. Calculate the volume of the solid obtained by rotating the region bounded by y = x ² – 4x + 5, x…

A: To calculate the volume of solid obtained by rotating the region bounded by the following curves:…

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: Find the volume of the solid obtained by rotating the region bounded by x = -3 + y² and x = -2y…

A: Given the curve is x=-3+y2, x=-2y Outer radius=-3+y2+9=y2+6 inner radius=-2y+9 Intersection point is…

Q: Find the volume of the solid formed by revolving the region bounded by the graphs y = √x and y = x^2…

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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 obtained by rotating the region bounded by the given curves about the…

A: We will find the volume of revolution as following.

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 formed by revolving the region bounded by the graphs of y = x2 + 1, y =…

A:

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

A: Given

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 generated by revolving the region bounded by the curves y = 1 – |x| and…

A:

Q: Determine the volume of the solid generated when the region bounded by the curve y² = x³, x = 2 and…

A: The region bounded by the curves y2=x3 and x=2, can be shown by the following image : If we put x=2…

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 obtained when the region above the x-axis, bounded by the x-axis, and…

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Q: Find the volume of the solid generated by revolving the region bounded by the y = 2x - x2 and y = 0…

A: Find out the volume of the solid generated by revolving the region by the y=2x-x2 and y=0 about the…

Q: Find the volume of the solid generated when the region bounded by y = 5x and y= 15√√x is revolved…

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 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: Q3: Calculate the volume of the solid obtained by rotating the region bounded by the curve y = 2x -x…

A:

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

A: Given : The curves y=x2+4x+5  , y = 0.   To determine : The volume of the solid obtained by rotating…

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 V of the solid formed by revolving the region bounded by the graphs of y= T – y = 0…

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Q: Find the volume of the solid generated by revolving about the x-axis the region bounded by the line…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the x2 -y2 = 9; x+y = 9; x…

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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…

A:

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

A:

Q: Calculate the volume of the solid obtained by rotating the region bounded by the curve y=2x-x² and…

A: Sketch the region and integrate in x variable.

Q: y = Vx + 1 + x and the x-axis from x = 0 to x = 3 about the y-axis.

A: When rotating about y axis, we should use shell method to find the volume. The formula for volume is…

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

A: Given curve: y= x3 At x=2, y =8 At x=0, y=0 We know that  The volume of the solid formed by…

Q: Determine the volume of the solid generated when the region bounded by the curve y²=x³ and the…

A: It is given that curves are y2=x3 and y=0 (i.e. x-axis) If these curves are drawn on a graph, they…

Q: Find the volume of the solid obtained by rotating the region bounded by x = 8 – y² - and x 2y about…

A: Given the region is bounded by the curves x=2y and x=8-y2 about the line x=9. The curves intersect…

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: Find the volume swept out by revolving the region bounded by the x-axis and the graph of x = 2t, y =…

A: Given that x = 2t and y = t(2–t). Obtain the interval of integration as follows.

Q: Find the volume of the solid formed by rotating the region enclosed by y = elx + 3, y = 0, x = 0, x…

A: Plot the curves and find the enclosed region. The shaded region represents the enclosed region.

Q: Find the volume of the solid formed by rotating the region bounded by the y.x=5 curve and the y…

A:

Q: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x-3y - 2 = 0…

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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.