Finding limits of integration for area of polar equations

[burt]

I'm learning how to find the area within polar equations. I know that the integral is: [MATH]\frac12\int^{\beta}_{\alpha}f(\theta)^2\ d\theta[/MATH]. But, how are [MATH]\alpha[/MATH] and [MATH]\beta[/MATH] found? Is it something that there is only one method for? Or, are there different strategies to use?

If the answer is that there is just one way, what is it? And, if there is no one-fits-all method, but multiple things to look at - what are they?

 

[MarkFL]

I'd say it depends on the problem, and what kind of symmetry you can apply, etc.

 

[Steven G]

I'm learning how to find the area within polar equations. I know that the integral is: [MATH]\frac12\int^{\beta}_{\alpha}f(\theta)^2\ d\theta[/MATH]. But, how are [MATH]\alpha[/MATH] and [MATH]\beta[/MATH] found? Is it something that there is only one method for? Or, are there different strategies to use?

If the answer is that there is just one way, what is it? And, if there is no one-fits-all method, but multiple things to look at - what are they?

You are trying to find the area so in this case the limits of integration, which are values of \(\displaystyle \theta\)'s, are the values that \(\displaystyle \theta\) goes between.