Find the volume “V” obtained by revolutionizing the region between y=2√x  y  y=x around the x=-2 axis

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

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Q: Draw the area bounded by function y = x^2 + 1 and line y = 5, then calculate the volume of the solid…

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

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Q: Find the volume of the solid generated of the area in the first quadrant bounded by y = 3x – x³, x =…

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Q: Find the volume of the solid of revolution formed by revolving the region bounded by y = f(x) = 2x -…

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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: The area bounded by y = 2x² - x³, and y=0 is revolved about x=0. Find the volume of the solid…

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Q: Find the volume of the solid formed by rotating the region enclosed by y = x3 and y = 4x in the…

A: We first sketch the region using a graphing calculator  y=x3 (blue) y=4x (green) The shaded region…

Q: Find the volume of the solid formed by revolving the region bounded by f (x) = 4x – x² and the…

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Q: Find the volume of the solid formed by rotating the region enclosed by у 3 е + 5, у — 0, х — 0, х —…

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Q: What is the volume obtained by rotating the region bounded by x = (y - 3)½ and y = 2x2 + 1 around…

A: Here we use basic definition of volume .

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

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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 when the region bounded by y = 2x², x = 0, x = 4, and y = 0 is revolved about the…

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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: 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 the solid generated when the region bounded by y = 4x and y = 16VX is revolved…

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Q: Find the volume of the solid that results when the region enclosed by x = y² and x = y is revolved…

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Q: Find the volume of the solid generated when the region bounded by y = 9 – x and y = 2x + 6 is…

A: To find the volume of solid generated by revolving around the x axis

Q: Find the volume formed by rotating the region enclosed by: 6.2y and y° = x with y > 0 about the…

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Q: ) Find the volume of the solid formed by revolving the region bounded by the cu y = √9-x² and y = 0…

A: To Find:  Volume of the solid formed by revolving the region bounded by the curve       y = 9 - x2 ,…

Q: Find the volume of the solid generated when the region bounded by y= 9x and y 27x is revolved about…

A: Given curves are y=9x   ....1 and y=27x  ...2

Q: Find the volume of revolution from the region bounded by y=x, x+y=6 and y=1, being revolved around…

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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 whose base is the region in the first quadrant bounded by y 1, and the…

A: Here, to find the volume of the solid whose base is the region in the first quadrant bounded by…

Q: Find the volume of the solid that results when the region enclosed by 4x 0, x = 1, and y = 0 is…

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

A: We need some modification I'm original formula to solve this problem. Let's see what modification we…

Q: Find the volume of the solid obtained by rotating the region bounded by y = 56x – 8x² and y = 0…

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Q: Find the volume of the solid that results when the region enclosed by x = y2 and y = x is revolved…

A: Find the volume of the solid that results when the region enclosed by x =y2 and y = x is revolved…

Q: Find the volume formed by rotating the region enclosed by: x = 7.8y and y = x with y > 0 about the…

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Q: Find the volume of the solid generated by revolving about the x-axis the area bounded by y=√(x), x=4…

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Q: Find the volume generated by rotating the region between the graphs of y = 2 - x, x = 0, and the…

A: Consider the provided region, y=2-x,x=0 Find the volume generated by rotating the region between the…

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

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Q: Find the volume obtained by rotating the area bounded by y=x^4 and y=1 around the line y=8

A: Graph y = x4, y = 1 and y = 8 to find the boundary points as follows.

Q: Find the volume of the solid obtained by rotating the region bounded by  y = 35x − 7x2  about the…

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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 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 when the region bounded by the y=√(3x) and y=√(3−x) is rotated about the x axis.

A: To calculate the volume of the region bounded by the given curves when rotated around x-axis.

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

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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 generated by revolving the region bounded by y = -2x² and y = x² – 3 ,…

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

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Q: find the volume “V” obtained by revolutionizing the region between y=x2  and y=12-x around the axis…

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Q: Find the volume of the solid generated when the region enclosed by y = sqrt(2x + 8), y = x, x = 0 is…

A: Given :     To find the volume of the solid.

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

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Q: Find the volume formed by rotating the region enclosed by:   x=8y  and  y^3=x  with  y≥0   about…

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

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Q: Find the volume of solid formed when the region bounded by y = x² and y = Vx are revolved about…

A: To find the volume of solid formed when the region bounded by y=x2 and are revolved about x-axis…

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.