Discuss the three methods for finding volume of a solid obtained by rotating a region about a given axis. Consider the functionf (x) = V4 – x defined over the interval [0, 4] is %3D rotated around the x-axis Discuss which of the three methods can be used to find the volume of the solid and set up the formula for finding the volume.

Q: Find the volume of the region between the graph of f(æ, y) = 9 – x² – y² and the æyplane. volume %3D

A: Given fx,y=9-x2-y2

Q: The base of a three-dimensional figure is bound by the x-axis and the curve y = et on the interval…

A:

Q: * A region is bounded by y = 10 – x2 and y = x – 2 part A Compute the area. This region is a base of…

A:

Q: How do you calculate the volume of a sphere if you know the radius? I need to make accurate to 2…

A: V=(4/3)pi5832 V=4pi1944 V=pi7776 now put pi=22/7 not 3.14 directly othwrise it will create error

Q: A volume is described as follows: 5 1. the base is the region bounded by y = 5 – a and y = 0 9 2.…

A: Volume of the region,

Q: Find the volume of the solid generated when the region under the curve y = 1/(x2 + 3x + 2) from x =…

A:

Q: The base of a solid is the region enclosed by the graph of y = vln x, the line x = e, and the…

A: Given,  The base of solid is the region enclosed by y=ln(x), the line x=e and the x-axis. Also…

Q: The base of a three-dimensional figure is bound by the line x = -y2-2y +3 on the interval [0, 1].…

A: Option(4) is true

Q: A volume is described as follows: 9 2 - -x² and y = 0 1. the base is the region bounded by y = 9 2.…

A:

Q: ded region if it is revolved around the x-axis.

A: answer is in next step

Q: x Let the region R be the area enclosed by the function f(x) = x² - 2, the horizontal line y = -3…

A:

Q: Find the volume of the solid obtained by rotating about the x-axis the region enclosed by the…

A: Find the volume of the solid obtained by rotating about the x-axis closed by the curves . y= secx…

Q: f(x) = 19 – x², x 20 f(x) = x - 3, x 2 0

A: We will find the volume as following.

Q: The region bounded by f(x) 2x² + 12x + 14, x = = 0 is rotated about the y-axis. Find the volume of…

A:

Q: R is the region bounded by the functions f(x) = x + 2 and the x-axis and the lines x=2 and x=4.…

A:

Q: A volcano and z = x² + y² fills the volume between the graphs z = 0 1 ²+2), and outside the cylinder…

A:

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.