How Do You Calculate the Area Bounded by a Polar Curve?

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Homework Help Overview

The discussion revolves around calculating the area bounded by a polar curve, specifically the equation r=6-4sin(θ). Participants are exploring the application of the area formula for polar coordinates and the correct bounds for integration.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to determine the bounds for integration, questioning whether they are correct in assuming the bounds are from 0 to 2π. They also express uncertainty about their calculations leading to an area of 63.5.
  • Another participant questions the relationship between the calculated area and the expected value of 44π.
  • Further discussion includes a participant reflecting on potential calculator errors and the importance of using radians instead of degrees.

Discussion Status

The discussion is active, with participants providing insights and suggestions for checking calculations. There is a recognition of the need to verify assumptions about angle measurement and the method of calculation. No explicit consensus has been reached regarding the correct area value.

Contextual Notes

Participants are navigating issues related to calculator settings and the interpretation of bounds in polar coordinates. The original poster's uncertainty about the bounds and the calculations indicates a need for clarification on these aspects.

will_lansing
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[SOLVED] Area of Polar Coordinates

Homework Statement


Find the area of the region bounded by r=6-4sin\Theta


Homework Equations


A=(1/2)\int r^{2} d\Theta


The Attempt at a Solution


I'm not sure what the bounds are but I thought they were 0 to 2pi. Am I wrong if so how then do you go about finding the bounds?
A=(1/2)\int [36-48sin\Theta+16sin^2\Theta d\Theta
A=(1/2)[36\Theta-48cos\Theta+8\Theta-4sin2\Theta]

and i got the answer to be 63.5 where did i go wrong?
 
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How do get 44\pi=63.5?
 
I'm not sure what i did. I think i typed in the wrong thing in my calculator or something. but i just plugged 2pi and 0 in for theta, but i still got the wrong answer. What am i suppose to do.
 
Do it by hand, then, and see if you get 44*pi.

One possible reason why your calc gave you something else than that might be that your calculator is measuring angles in degrees instead of radians.
 
yeah you're right i forgot to change back to radians, i feel so stupid now. well thanks, maybe i should just do by hand and not put so much trust in the calculator.
 

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