Integrating to find Volume (different from the other guy)

In summary, the conversation is about finding the volume of a solid obtained by rotating a region bounded by two curves about a specified line. The person is attempting to use the shell method but is having trouble setting up the integral due to the region being integrated about x=-4. They request for clarification or assistance on finding the shell radius.
  • #1
CB4
10
0
Ok so I'm doing my online homework and I came across this problem:

"Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

y=11, y=x+28/x

about x=-4"


So I attempted to use the shell method to solve this equation but I get confused on how to set up my integral. I don't really know how to tackle the region I'm integrating about (x=-4).
 
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  • #2
Are you having trouble finding the shell radius, or something else? If you could be more specific, or show your work, it would be easier to help.
 

What is the purpose of integrating to find volume?

The purpose of integrating to find volume is to calculate the total space occupied by a three-dimensional object. This is useful in various fields, such as engineering, physics, and chemistry, where accurately determining the volume of an object is necessary for further calculations or experiments.

How is integrating used to find volume?

Integrating is used to find volume by breaking down the three-dimensional object into infinitesimally small slices, determining the area of each slice, and then summing up all the areas using integration. This allows for an accurate calculation of the total volume of the object.

What are the steps involved in integrating to find volume?

The steps involved in integrating to find volume include identifying the limits of integration, determining the function that represents the cross-sectional area of the object, setting up the integral, and evaluating the integral using appropriate integration techniques.

What are the different integration techniques used to find volume?

There are various integration techniques that can be used to find volume, including the disk method, the shell method, and the washer method. These techniques differ in the shape of the infinitesimal slices used and the way the integral is set up.

Are there any limitations or assumptions when using integration to find volume?

One limitation of using integration to find volume is that it assumes the object has a uniform cross-sectional area throughout its entire length. This may not be the case for complex or irregularly shaped objects. Additionally, integration may not be suitable for objects with varying density or composition.

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