- #1
Finding the Area Enclosed by a Polar Curve
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Homework Help Overview
The discussion revolves around finding the area enclosed by a polar curve, specifically involving the integration of a function defined in polar coordinates. Participants are exploring the correct limits of integration and the setup for the problem.
Discussion Character
- Exploratory, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Participants discuss the integration limits and question the choice of limits from -π/2 to 0. There is an exploration of whether a sketch has been made and what values of θ correspond to negative r values for the inner loop. Some participants suggest alternative limits involving arcsin, while others confirm the correctness of these limits.
Discussion Status
The discussion is active, with participants providing guidance on the limits of integration and confirming the correctness of proposed values. There is a mix of interpretations regarding the setup, but productive dialogue is ongoing.
Contextual Notes
Participants mention potential mistakes in their initial approaches and express uncertainty about the limits of integration, indicating a need for clarification on the polar curve's behavior.
- #2
LCKurtz
Science Advisor
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amninder15 said:
Why did you choose ##-\frac \pi 2## to ##0##? Just guessing? Have you drawn a sketch? Do you know what ##\theta## give negative ##r## values for the inner loop?
- #3
- #4
DryRun
Gold Member
- 837
- 4
Your graph is correct for ##\theta## varies between 0 and 2pi. Now, generally how do you find the area of a polar region?
- #5
LCKurtz
Science Advisor
Homework Helper
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amninder15 said:
Yes. Those are the correct limits. Ugly or not, just plow ahead and you will get one of the answers listed.
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