Finding area between two curves Polar Coordinates

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Homework Help Overview

The discussion revolves around finding the area between two curves defined in polar coordinates: the circle given by r = 3sinθ and the carotid curve defined by r = 1 + sinθ. Participants are exploring the setup for calculating the area between these curves.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants have graphed the curves and identified their points of intersection at π/6 and 5π/6. There is uncertainty about the correct approach to set up the integral for the area calculation, particularly concerning the area of the carotid curve that lies below the x-axis. Questions arise about the validity of using the integral of (3sinθ - (1 + sinθ)) with the specified limits of integration.

Discussion Status

Some participants have provided feedback on the proposed approach, indicating that it seems reasonable but also cautioning against the choice of integrand. There is a mix of exploration and guidance, with some participants affirming the need to verify the integrand used for the area calculation.

Contextual Notes

Participants are discussing the implications of the carotid curve's area being beneath the x-axis and how this affects the setup of the integral. There is also mention of using online tools for checking work, indicating a desire for validation of their calculations.

PsychonautQQ
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Homework Statement


Find the area inside the circle r = 3sinθ and outside the carotid r = 1 + sinθ




The Attempt at a Solution


Alright so I graphed it and found that they intersect at ∏/6 and 5∏/6.
I can't think of a good way to approach the problem. The carotid has some of it's area beneath the x-axis otherwise I would take the area of the 3sinθ - the area of the other one. Will it work if set the limits of integration to pi/6 and 5pi/6 and take the integral of (3sinθ - (1+sinθ)? I'm a bit lost
 
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PsychonautQQ said:

Homework Statement


Find the area inside the circle r = 3sinθ and outside the carotid r = 1 + sinθ




The Attempt at a Solution


Alright so I graphed it and found that they intersect at ∏/6 and 5∏/6.
I can't think of a good way to approach the problem. The carotid has some of it's area beneath the x-axis otherwise I would take the area of the 3sinθ - the area of the other one. Will it work if set the limits of integration to pi/6 and 5pi/6 and take the integral of (3sinθ - (1+sinθ)? I'm a bit lost

Yes, that all seems reasonable. Just compute your integral and you're done.
 
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I got 1.369705. Is there any online integral doer I can use to check my work?
 
PsychonautQQ said:
I got 1.369705. Is there any online integral doer I can use to check my work?

Yes, that's the correct answer. Wolfram alpha is good for checking your work afterwards.
 
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Likes   Reactions: 1 person
PsychonautQQ said:

Homework Statement


Find the area inside the circle r = 3sinθ and outside the carotid r = 1 + sinθ




The Attempt at a Solution


Alright so I graphed it and found that they intersect at ∏/6 and 5∏/6.
I can't think of a good way to approach the problem. The carotid has some of it's area beneath the x-axis otherwise I would take the area of the 3sinθ - the area of the other one. Will it work if set the limits of integration to pi/6 and 5pi/6 and take the integral of (3sinθ - (1+sinθ)? I'm a bit lost

NO. That's the wrong integrand. Look up the formula for polar area.
 

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