Finding the area enclosed by r=3sin theta

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Homework Help Overview

The problem involves finding the area enclosed by the polar curve defined by r = 3sin(θ). Participants are discussing the appropriate method for calculating the area in polar coordinates.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to evaluate the area using an integral approach but questions the validity of their result. Some participants suggest that the area calculation might yield zero and recommend drawing a picture for better understanding. There is also a discussion about the correct formula for area in polar coordinates.

Discussion Status

The discussion is ongoing, with participants questioning the assumptions made about the area formula. Some have provided guidance on the correct approach, while others are exploring different interpretations of the area calculation.

Contextual Notes

There seems to be confusion regarding the formula for area in polar coordinates, with participants debating the correct expression to use. The original poster acknowledges a mistake in recalling the formula.

grog
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Homework Statement



Find the area enclosed inside r=3 sin (theta)

Homework Equations



integral?

The Attempt at a Solution



basically, I took \int3sin\Theta from 0 to 2pi, then pulled the 3 out to get

3\int sin\Theta from 0 to 2pi and then

3[-cos(\Theta)] evaluated from 0 to 2pi.

that seems too easy. what am I missing?
 
Last edited:
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Who said everything has to be super hard? But if you work that out, you'll get 0 for the area. Is that right? It might help to draw a picture. And, hey, area in polar coordinates isn't the integral of r dtheta, is it? Would you look up the right formula for area?
 
Last edited:
ah. that's what it was. I forgot about the formula for area. : (

Thanks!
 
Dick said:
Who said everything has to be super hard? But if you work that out, you'll get 0 for the area. Is that right? It might help to draw a picture. And, hey, area in polar coordinates isn't the integral of r dtheta, is it?
Well, actually, Dick, area in polar coordinates is r dtheta! You didn't say quite what you meant to, did you?

Would you look up the right formula for area?
 
HallsofIvy said:
Well, actually, Dick, area in polar coordinates is r dtheta! You didn't say quite what you meant to, did you?

Are you SURE?
 
The integral of r*dtheta*dr is the area. Not the integral of r*dtheta. I missed it at my first reading as well.
 

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