What method to use to calculate volume

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  • Thread starter Thread starter thushanthan
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    Method Volume
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SUMMARY

The discussion centers on the methods for calculating volume using Single Variable Calculus and Multivariable Calculus. Single Variable Calculus, specifically through Solids of Revolution, is simpler for straightforward rotational volumes, while Multivariable Calculus employs Double and Triple Integrals for more complex shapes. The choice of method depends on the geometry of the object; if it involves simple rotations, Single Variable methods are preferred, whereas Multivariable methods are necessary for more intricate volumes. Understanding both approaches allows for flexibility in solving volume problems.

PREREQUISITES
  • Single Variable Calculus: Solids of Revolution
  • Multivariable Calculus: Double Integrals
  • Multivariable Calculus: Triple Integrals
  • Understanding of volume calculation techniques
NEXT STEPS
  • Study the application of Single Variable Calculus in calculating volumes of solids of revolution
  • Explore the use of Double Integrals in Multivariable Calculus for volume calculations
  • Learn about Triple Integrals and their applications in complex volume problems
  • Investigate the relationship between Single and Multivariable methods in volume calculations
USEFUL FOR

Students and educators in mathematics, particularly those focusing on calculus, as well as professionals in fields requiring volume calculations, such as engineering and physics.

thushanthan
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Hi

Can anyone explain to me the difference between the following:

Single variable Calculus : Solids of Revolution

Multivariable : Double and Triple Integrals.

When I tried to connect these topics, I found the same answer : Volume.

My question is how to decide on the method to use? Thank you!
 
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You can actually use multivariable calculus to prove the volume identities in single variable. If we don't have a simple rotation of a two-dimensional object, then we resort to multivariable, otherwise, it's simpler to use the single variable methods, thought it takes more effort to remember and they're just special cases of the multivariable method.
 
thanks!
 

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