Troubleshooting Trigonometric Substitution for Circle Area Calculation

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SUMMARY

The discussion centers on troubleshooting the calculation of the area of a circle using trigonometric substitution. The user initially set x = r*cos(theta) but encountered an incorrect result of area = -πr^2 due to improper limits of integration. By switching to x = r*sin(theta), the user achieved the correct area calculation. The key takeaway is the importance of correctly defining limits of integration in trigonometric substitution.

PREREQUISITES
  • Understanding of trigonometric substitution in calculus
  • Familiarity with integral calculus and area calculations
  • Knowledge of limits of integration
  • Basic trigonometric identities and functions
NEXT STEPS
  • Review the concept of trigonometric substitution in calculus
  • Study the correct application of limits of integration in definite integrals
  • Practice calculating areas using different trigonometric identities
  • Explore common pitfalls in integral calculus and how to avoid them
USEFUL FOR

Students and educators in calculus, mathematicians interested in integral techniques, and anyone looking to deepen their understanding of trigonometric substitution methods in area calculations.

basenne
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I was messing around proving the area of a circle using trigonometric substitution. However, I ended up with area = -πr^2.

In my integral I ended up using trigonometric substitution and setting x = r*cos(theta)

However, this yields x = -r*sin(theta)*d(theta).

When that's substituted back into my integral, I ended up with the negative value for area. Why is it that if I were to use a different angle theta and express x = r*sin(theta) that I end up with the correct area?

Thanks a lot, as always.
 
Physics news on Phys.org
hi basenne! :smile:

it's probably your limits of integration that were wrong …

what exactly was your integral?​
 

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