Find the volume generated by revolving the area bounded by xy=4, x=1, x=4 and the x-axis about the y-axis. * A

Q: Determine the volume of the rotating object that occurs if the area of ​​the curve y1 = - x2 + 4 and…

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Q: Find the volume generated by revolving bout the line y = -1 the area bounded by (x - 2)2 = 4(y + 2)…

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Q: Calculate exactly the volume of the solid obtained by rotating the area delimited by y=(x-2)^2 and…

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Q: Revolve the region between y=x-x4 and y=0 about the y-axis. Find area

A: The given region is between y=x-x4 and y=0 and it is revolved around y- axis.

Q: om

A: Computing the volume generated by rotating the area through one revolution about the x-axis.…

Q: b) y = x +1, y = x °+1 (in the first quadrant), about the x-axis. (method of shells)

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Q: revolving th 4x and stra

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Q: Find the Volume of the region bounded by the graphs of y=√x and y=2sinx+1 and the x-axis with…

A: Given function fx=x and y=2sinx+1 and x-axis. We have to find the volume of region bounded by the…

Q: the area bounded by the parabola y ² =4ax, the y-axis, and the line y=2a revolves about the line…

A: given that the region is bounded byy2=4ax and y=2a and  revolves about y=2a Graphically,

Q: Find volume if area enclosed is rotated about y= -2.

A: To find the volume if the area enclosed by the below curves is rotated about y = -2.

Q: Find the volume generate

A: Given,      y=-x4+3x3,  y=0 revolving about yhe y-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.