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

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SUMMARY

The discussion centers on the necessity of drawing graphs when solving Disk, Washer, and Shell method problems in calculus. Participants argue that while graphs serve as visual aids to ensure correct integral setup, skipping this step due to concerns about accuracy is not advisable. Instead, improving graphing skills is emphasized as essential for accurately identifying the equations involved in the problem. Ultimately, the consensus is that graphing is a critical component of the problem-solving process.

PREREQUISITES
  • Understanding of Disk, Washer, and Shell methods in calculus
  • Basic skills in sketching mathematical graphs
  • Familiarity with integral calculus concepts
  • Ability to interpret and manipulate equations
NEXT STEPS
  • Practice sketching graphs for various functions to improve accuracy
  • Review integral calculus techniques related to volume calculations
  • Explore online resources or tutorials on the Disk, Washer, and Shell methods
  • Engage in problem-solving exercises that require graphing for verification
USEFUL FOR

Students studying calculus, educators teaching integral methods, and anyone looking to enhance their mathematical problem-solving skills through effective graphing techniques.

Vividly
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Solving the problem
Is there a way to solve a Disk,Washer,Shell method problem without actually creating a graph?
 
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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.
 
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