Finding area in polar coordinates

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Homework Help Overview

The discussion revolves around finding the area of regions defined in polar coordinates, specifically focusing on the rose curve described by the equation r=4cos(3θ) and another area between two curves, r=sqrt(cos(2θ)) and r=2cos(θ).

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the setup of the integral for calculating area in polar coordinates, with one participant expressing confusion over the integration process and the resulting area. Questions arise regarding the limits of integration and how they affect the area calculation. Another participant raises a related question about finding the area between two different polar curves, indicating difficulties in achieving expected results.

Discussion Status

The discussion is ongoing, with participants sharing their results and questioning the correctness of their approaches. Some participants have arrived at the same numerical result, suggesting a potential common misunderstanding. There is also an exploration of the necessary limits of integration for the polar curves, indicating a productive direction in clarifying the problem setup.

Contextual Notes

There is mention of specific identities used in the integration process and the potential for confusion regarding the limits of integration, which are not explicitly stated in the posts. Participants are also grappling with the implications of their calculations leading to unexpected results.

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Homework Statement


"Find the area of the region described: The region that is enclosed by the rose r=4cos3[theta]"

Homework Equations



A= [integral] (1/2)r^2 d[theta]

The Attempt at a Solution



I'll use Q as [theta]..

I'm not really sure, but I set up (1/2) [integral] (16(cos^2)3Q) dQ

.. then I thought we were supposed to use the identity (cos^2)Q = (1/2)(1+cos2Q), but every time I substitute this in and integrate, I get 8[pi] instead of 4[pi], the correct answer. What am I doing wrong?

Thank you so much :]
 
Last edited:
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I get 8pi as well.
 
hmmm, I asked someone else and they got 8pi too...


Well I had one more question... if I were finding the area between
r = sqrt[cos2(theta)] and
r = 2cos(theta)

do I basically do the same thing as finding the area between two regular curves? Each time I try it, I come up with zeros and I feel like that can't be right :[
 
That's a really weird graph intersection. Where did you get that question from?
 
You don't say anything about what limits of integration you used. \theta going from 0 to what traces that figure exactly once?
 

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