The boundaries of doule integrals in polar form

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SUMMARY

The discussion focuses on determining the bounds for a double integral in polar coordinates, specifically for the area enclosed by the cardioid defined by the equation r = 3 + 3sin(θ). The inner integral's bounds are established as 0 to 3 + 3sin(θ), while the outer integral's bounds require finding the appropriate limits for θ. Participants suggest graphing the cardioid and substituting specific θ values to clarify the outer bounds.

PREREQUISITES
  • Understanding of polar coordinates and their representation.
  • Familiarity with double integrals and their applications in area calculations.
  • Basic knowledge of graphing polar equations, particularly cardioids.
  • Proficiency in evaluating integrals, especially in polar form.
NEXT STEPS
  • Learn how to graph polar equations, focusing on cardioids.
  • Study the process of setting up double integrals in polar coordinates.
  • Explore techniques for determining bounds in double integrals.
  • Investigate examples of area calculations using double integrals in polar form.
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Mathematics students, educators, and professionals involved in calculus, particularly those working with polar coordinates and double integrals.

winbacker
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Hi I need to use a double integral to find the area of the region bounded by:

r = 3 + 3sinQ where Q = theta.

I know the bounds of the inner integral are from 0 to 3 + 3sinQ.

However, I do not know how to determine the bounds of the outer integral.

Any help would be greatly appreciated.
 
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Ok this seems to be a cardioid. What you found were the boundaries of r. So Where is the problem of finding theta? Just graph it. If all else fails plug in some values of theta.
 

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