Choose a method to find the VOLUME of the solid obtained by rotating the region bounded by he given curves around the indicated line. Include both a 2-D and 3-D picture. State the definite ntegral. Show all work in exact form. xy = 1, y = 0,x = 1,x = 2; about x = -1

Q: Write the equation for the volume obtained by rotating the region shaded below about the line y =…

A: Hee, the volume formula is: V=π∫ab((f(x)-a)2-(g(x)-a)2) dx where the region bounded by the curves…

Q: Ris the region bounded by the functions f(x) = 2? +1 and the g(x) = – 2 and the lines x=1 and x=3.…

A: Given that  f(x)=x^2+1,g(x)=x-2 To find the volume of the region

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

A: Let S be the solid obtained by rotating the region R bounded by the curves y=x2, y=1 and x=2 about…

Q: 1. Graph and shade the region enclosed by the curves x=(y-2) and y= x . Find the volume of the solid…

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

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Q: 1.

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Q: Compute the volume of the solid formed by revolving the given region about the given line. Region…

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Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

A: Sketch the region and typical shell

Q: Determine the volume of a solid produced by rotating about the line y=14.9 the region bounded by the…

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Q: Two curves having an equation of x = 2 vy and y = 2 vx intersect each other. Compute the centroid of…

A: Given,           x=2y    and     y=2x

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.