Finding this volume without cylindrical shells

In summary, the conversation discusses the possibility of solving a problem without using cylindrical shells. The problem involves finding the volume of a region bounded by a curve and the x-axis, rotated around the y-axis. The individual has attempted to solve it using cylindrical shells but is now wondering if it can be done without them. After trying for an hour, they are seeking advice on how to approach the problem. However, they later state that they have figured it out.
  • #1
member 508213
This is not a homework problem this is just a problem I was thinking about whether or not it would be possible to solve without cylinderical shells

The region bounded by y=1/(x^2) x=e x=e^3 and the x-axis Rotated around y axis.. I did cylindrical shells and got 4pi and then wondered if I could do without.

I have been trying to figure out how to do it for about an hour but can't come up with anything that works.

Is it possible to do by hand without cylinderical shells? If so I would like so advice on how to go about it.
 
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  • #2
Never mind I got it
 

What is the concept of finding volume without cylindrical shells?

The concept of finding volume without cylindrical shells involves using a different method, such as integration, to calculate the volume of a three-dimensional object without using cylindrical shells as the base. This method is often used in calculus and can be applied to various shapes and objects.

Why would one want to find the volume without cylindrical shells?

Finding the volume without cylindrical shells can be useful in situations where the object being measured does not have a cylindrical shape or when using cylindrical shells is not an efficient method. It can also be a way to practice and strengthen understanding of integration in calculus.

What are some common shapes that can be measured using this method?

This method can be applied to a variety of shapes, such as spheres, cones, pyramids, and more complex shapes that cannot be easily divided into cylindrical shells. It can also be used for irregularly shaped objects by breaking them down into smaller, simpler shapes.

What are the steps involved in finding volume without cylindrical shells?

The steps may vary depending on the shape being measured, but generally involve setting up an integral with the appropriate bounds and integrand, evaluating the integral, and simplifying the result to get the volume. It is important to have a good understanding of calculus and geometry in order to successfully apply this method.

Are there any limitations to using this method?

While finding volume without cylindrical shells can be a useful method, it may not always be the most efficient or accurate method for measuring volume. For complex shapes, the integral may be difficult or impossible to evaluate, and for objects with curved surfaces, the result may not be as precise as using cylindrical shells. It is important to consider the limitations and accuracy needed for the specific situation before using this method.

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