Find the volume of the solid generated by revolving the region bounded by the graphs of the following equations about the indicated line. Draw a picture of the region to be rotated along with a representative rectangle. Clearly indicate the METHOD that you are using. Give a brief explanation of why you chose to use that particular method. Then, find the volume.   y= x^2, y= 2x, about the line x= -2.

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

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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: 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: Calculate the total area of the region described. Do not count area beneath the x-axis as negative.…

A: the area is given by A=∫ab|fx-gx|dx here we have fx=7x g(x)=0 a=0, b=16

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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

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Q: Let the region R be the area enclosed by the function f(x) = 2x³ , the horizontal line y = –3 and…

A: Given the region R be the area bounded by fx=2x13,y=-3,x=0,x=3. Visualize the solid: Each…

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.