Can you solve a Disk, Washer, Shell method problem without drawing a graph?

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• Vividly
In summary, the conversation discusses the possibility of solving a Disk, Washer, Shell method problem without creating a graph. One person argues that drawing a graph is important for ensuring correct integration, while the other person suggests that not being able to draw the graph perfectly may lead to mistakes. The expert summarizer points out that avoiding drawing the graph is not a valid solution and suggests learning how to make a useful graph instead. An analogy is used to further illustrate this point.
Vividly
TL;DR Summary
Solving the problem
Is there a way to solve a Disk,Washer,Shell method problem without actually creating a graph?

Isn't the graph just a visual aid to insure you've setup the integrals correctly?

I'm sure it will give you extra points should you get the wrong answer but have visualized it correctly meaning you should do it for that additional reason alone.

Vividly said:
Is there a way to solve a Disk,Washer,Shell method problem without actually creating a graph?
Why would you want to not draw a graph?

Mark44 said:
Why would you want to not draw a graph?
Because sometimes I may not draw the graph perfectly and may miss which equation is suppose to be subtracted from the other. I had this happen before.

Vividly said:
Because sometimes I may not draw the graph perfectly and may miss which equation is suppose to be subtracted from the other. I had this happen before.
Not wanting to sketch a graph because you might not do it perfectly is a terrible reason. If you have a problem drawing the graph correctly, the solution is not to skip this important step -- it's to learn how to make the graph good enough to be useful.

What you're saying sounds to me like a situation where somebody needs to get a bunch of items at the store, but doesn't want to write down the list of items because of poor handwriting ability.

Last edited:

What is the Disk Method?

The Disk Method is a mathematical technique used to find the volume of a solid of revolution, created by rotating a two-dimensional shape around an axis. It is also known as the "cylindrical shell method" or "washer method".

What is the Washer Method?

The Washer Method is a variation of the Disk Method, used when the shape being rotated has a hole in the center. This method involves subtracting the volume of the hole from the volume of the solid.

What is the Shell Method?

The Shell Method is another variation of the Disk Method, used when the shape being rotated is not a complete circle. This method involves finding the volume of cylindrical shells created by slicing the shape into thin vertical strips.

What are the differences between the Disk, Washer, and Shell methods?

The main difference between these methods is the shape of the cross-section being rotated. The Disk Method is used for circular cross-sections, the Washer Method is used for circular cross-sections with a hole, and the Shell Method is used for non-circular cross-sections.

What are some real-life applications of the Disk, Washer, and Shell methods?

These methods are commonly used in engineering and physics to calculate volumes of objects with rotational symmetry, such as cylinders, cones, and spheres. They can also be applied in fields such as architecture and manufacturing to determine the amount of material needed for a curved structure or object.

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